Peter Lancaster

Professor Emeritus

Department of Mathematics and Statistics

DSc

University of Liverpool, 1987

PhD

University of Singapore, 1964

MSc

University of Liverpool, 1956

BSc

University of Liverpool, 1952

Contact information

Email

lancaste@ucalgary.ca

Phone

Office: 403.220.6302

Office : MS426

Publications

Book

• Gohberg, Israel, Lancaster, Peter and Rodman, Leiba. Indefinite Linear Algebra with Applications Birkh\"auser Verlag, 2005. 357. Print.
• Lancaster, Peter. My life and mathematics 130. Birkh\"auser, 2002. 1-7. Print.
• Lancaster, Peter. The role of the {H}amiltonian in the solution of algebraic {R}iccati equations 25. Birkh\"auser, 1999. 157-172. Print.
• Lancaster, Peter, Maroulas, John and Zizler, Peter. The numerical range of selfadjoint matrix polynomials 106. Birkh\"auser, 1998. 291-304. Print.
• Lancaster, Peter and Matsaev, V.. Definitizable {$G$}-unitary operators and their applications to operator polynomials 87. Birkh\"auser, 1996. 222-232. Print.
• Lancaster, Peter and Matsaev, V.. Perturbations of {$G$}-selfadjoint operators and operator polynomials with real spectrum 87. Birkh\"auser, 1996. 207-221. Print.
• Lancaster, Peter and Salkauskas, Kes. Transform methods in applied mathematics , John Wiley \& Sons Inc., 1996. xii+332. Print.
• Lancaster, Peter and Rodman, Leiba. Algebraic Riccati Equations Oxford: Clarendon Press, 1995. 480. Print.
• Lancaster, Peter and Rodman, Leiba. Algebraic {R}iccati equations , The Clarendon Press Oxford University Press, 1995. xviii+480. Print.
• Lancaster, Peter and Rodman, Leiba. Solutions of the continuous and discrete-time algebraic {R}iccati equations: a review , Springer, 1991. 11-51. Print.
• Lancaster, Peter and Ye, Qiang. Variational properties and {R}ayleigh quotient algorithms for symmetric matrix pencils 40. Birkh\"auser, 1989. 247-278. Print.
• Koltracht, I. and Lancaster, Peter. Condition numbers of {T}oeplitz and block {T}oeplitz matrices 18. Birkh\"auser, 1986. 271-300. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. Invariant subspaces of matrices with applications , John Wiley \& Sons Inc., 1986. xviii+692. Print.
• Lancaster, Peter and Salkauskas, Kes. Curve and surface fitting Academic Press Inc. [Harcourt Brace Jovanovich Publishers], 1986. xii+280. Print.
• Lancaster, Peter and Tismenetsky, Miron. The theory of matrices , Academic Press Inc., 1985. xv+570. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. A sign characteristic for selfadjoint rational matrix functions 58. Springer, 1984. 363-369. Print.
• Lancaster, Peter and Gohberg, Israel. Silly math Academic Press Inc. [Harcourt Brace Jovanovich Publishers], 1983. 300. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. Matrices and indefinite scalar products 8. Birkh\"auser Verlag, 1983. xvii+374. Print.
• Barnett, S. and Lancaster, Peter. Matrices having striped inverse Hemisphere, 1982. 333-336. Print.
• Lancaster, Peter. A review of some recent results concerning factorization of matrix and operator valued functions 80. Dekker, 1982. 117-139. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. Matrix polynomials Academic Press Inc. 1982. SIAM, 2009., 1982. xiv+409. Print.
• Lancaster, Peter. Composite methods for generating surfaces 49. Reidel, 1979. 91-102. Print.
• Lancaster, Peter. Moving weighted least-squares methods 49. Reidel, 1979. 103-120. Print.
• Lancaster, Peter. A review of numerical methods for eigenvalue problems nonlinear in the parameter Birkh\"auser, 1977. 43-67. Internat. Schriftenreihe zur Numer. Math., Vol. 38. Print.
• Lancaster, Peter and Watkins, David S.. Interpolation in the plane and rectangular finite elements Birkh\"auser, 1976. 125-145. Internat. Ser. Numer. Math., Vol. 31. Print.
• Terray, John and Lancaster, Peter. A boundary value problem from the study of heat transfer Birkh\"auser, 1975. 303-308. Internat. Schriftenreihe Numer. Math., Band 27. Print.
• Lancaster, Peter. Spektraleigenschaften von {O}peratorfunktionen Birkh\"auser, 1970. 53-60. Internat. Schriftenreihe Numer. Math., Vol. 15. Print.
• Lancaster, Peter. Theory of matrices Academic Press, 1969. xii+316. Print.
• Lancaster, Peter. Lambda-matrices and vibrating systems , Pergamon Press, 1966. xiii+196. Print.
• Lancaster, Peter. Lambda-matrices and vibrating systems (1966 and 2002). Pergamon. Dover Publications Inc., 1966. xx+193. Print.

Journal article

• Freitas, P. and Lancaster, Peter. "On the optimal spectral abscissa for a system of linear oscillators.". SIAM Journal of Matrix Analysis and Applications 21. (2010): 195-208. Print.
• Lancaster, Peter and Tisseur, F.. "Hermitian quadratic matrix polynomials: solvents and inverse problems.". Linear Algebra and its Applications (to appear), Print.
• Boulton, L. and Lancaster, Peter. "Schur decomposition of a matrix and the boundary of the pseudospectrum.". SIAM J. Matrix Anal. and Appl.. (to appear), Print.
• Lancaster, Peter and Zaballa, I.. "A review of canonical forms for selfadjoint matrix polynomials.". Operator Theory: Advances and Applications (to appear), Print.
• Lancaster, Peter and Zaballa, I.. "Parametrizing structure preserving transformations of matrix polynomials.". Operator Theory: Advances and Applications (to appear), Print.
• Amiraslani, A., Corless, Rob, Lancaster, Peter and Amiraslani, Amirhossein. "Linearization of matrix polynomials expressed in polynomial bases". IMA Journal of Numerical Analysis, (2009). Print.
• Lancaster, Peter and Zaballa, I.. "Diagonalizable quadratic eigenvalue problems.". Mech. Systems and Signal Processing. 23. (2009): 141-157. Print.
• Amiraslani, A. and Lancaster, Peter. "Rayleigh quotient algorithms for nonsymmetric matrix pencils.". Numerical Algorithms. 51. (2009): 5-22. Print.
• Lancaster, Peter. "Model updating for self-adjoint quadratic eigenvalue problems.". Linear Algebra and its Applications 428. (2008): 2778-2790. Print.
• Lancaster, Peter. "Linearization of regular matrix polynomials". Electronic Journal of Linear Algebra 17. (2008): 21-27. Print.
• Boulton, L., Lancaster, Peter and Psarrakos, P.. "On pseudospecrta of matrix polynomials and their boundaries.". Math. of Computation 77. (2008): 313-334. Print.
• Lancaster, Peter. "Inverse spectral problems for semi-simple damped vibrating systems.". SIAM J. Matrix Anal. and Appl.. 29. (2007): 302-327. Print.
• Lancaster, Peter and Prells, U.. "Isospectral families of high-order systems". Z. Angew. Math. Mech.. 87. (2007): 219-234. Print.
• Lancaster, Peter, Prells, U. and Rodman, L.. "Canonical structures for palindromic matrix polynomials". Operators and Matrices 1. (2007): 469-489. Print.
• Wu, J-W.,, Lian, K-Y., and Lancaster, Peter. "A stabilization criterion for matrices.". Linear Algebra and its Applications. 422. (2007): 22-28. Print.
• Bohl, E. and Lancaster, Peter. "Implementation of a Markov model for phylogenetic trees.". Journal of Theoretical Biology 239.3 (2006): 324-333. Print.
• Lancaster, Peter and Psarrakos, P.. "On the pseudospectra of matrix polynomials.". SIAM Journal of Matrix Analysis and Applications 27. (2005): 115-129. Print.
• Lancaster, Peter and Rodman, L.. "Canonical forms for symmetric/skewsymsmetric real matrix pairs under strict equivalence and congruence.". Linear Algebra and its Applications 406. (2005): 1-76. Print.
• Guo, Chun-Hua and Lancaster, Peter. "Algorithms for hyperbolic quadratic eigenvalue problems.". Mathematics of Computation 74. (2005): 1777-1791. Print.
• Prells, U. and Lancaster, Peter. "Isospectral vibrating systems. Part II: Structure preserving transformations.". Operator Theory: Advances and Applications 163. (2005): 275-298. Print.
• Lancaster, Peter. "Isospectral vibrating systems. Part I: The spectral method.". Linear Algebra and its Applications. 409. (2005): 51-69. Print.
• Lancaster, Peter and Rodman, L.. "Canonical forms for hermitian matrix pairs under strict equivalence and congruence.". SIAM Review. 47. (2005): 407-443. Print.
• Lancaster, Peter and Prells, U.. "Inverse problems for damped vibrating systems.". Journal of Sound and Vibration 283. (2005): 891-914. Print.
• Farkas, A., Lancaster, Peter and Rozsa, P.. "Approximation of positive matrices by transitive matrices.". Computers and Mathematics with Applications 50. (2005): 1033-1039. Print.
• Lancaster, Peter and Psarrakos, P.. "Normal and seminormal eigenvalues of matrix functions.". Integral Equations and Operator Theory 41. (2003): 331-342. Print.
• Lancaster, Peter, Markus, A. S. and Zhou, F.. "Perturbation theory for analytic matrix functions: the semisimple case.". SIAM Journal of Matrix Analysis and Applications 25. (2003): 606-626. Print.
• Lancaster, Peter and Zhou, Fei. "A wider class of stable gyroscopic systems". Linear Algebra and its Applications 370. (2003): 257-267. Print.
• Farkas, Andr, Lancaster, Peter and R{\'o}zsa, P. "Consistency adjustments for pairwise comparison matrices". Numerical Linear Algebra with Applications 10.8 (2003): 689-700. Print.
• Bohl, Erich and Lancaster, Peter. "Irreversible Markov processes for phylogenetic models". Numerical Linear Algebra with Applications 10.7 (2003): 577-593. Print.
• Lancaster, Peter, Markus, A.S. and Psarrakos, P.. "Repeated eigenvectors and the numerical range of self-adjoint quadratic operator polynomials". Integral Equations and Operator Theory 44.2 Dover Publications Inc., (2002): 243-253. Print.
• Lancaster, Peter and Psarrakos, P.. "The numerical range of self-adjoint quadratic matrix polynomials". SIAM Journal on Matrix Analysis and Applications 23.3 Birkhauser, (2002): 615-631. Print.
• Lancaster, Peter. "Stabilization of gyroscopic systems". ZAMM. Zeitschrift f\"ur Angewandte Mathematik und Mechanik. Journal of Applied Mathematics and Mechanics 81.10 Birkhauser, (2001): 675-681. Print.
• Lancaster, Peter. "Normal and seminormal eigenvalues of matrix functions". Integral Equations and Operator Theory 41.3 Birkhauser, (2001): 331-342. Print.
• Lancaster, Peter and Markus, A.S.. "A note on factorization of analytic matrix functions.". Operator Theory: Advances and Applications 122. (2001): 323-330. Print.
• Kliem, W., Lancaster, Peter and Pommer, C.. "A precise bound for gyroscopic stabilization". ZAMM. Zeitschrift f\"ur Angewandte Mathematik und Mechanik. Journal of Applied Mathematics and Mechanics 80.8 Birkhauser, (2000): 507-516. Print.
• Dai, Hua and Lancaster, Peter. "Preconditioning block {L}anczos algorithm for solving symmetric eigenvalue problems". Journal of Computational Mathematics. An International Journal on Numerical Methods, Analysis and Applications 18.4 Birkhauser, (2000): 365-374. Print.
• Lancaster, Peter and Kliem, W.. "Comments on stability properties of conservative gyroscopic systems". American Society of Mechanical Engineers. Transactions of the ASME. Journal of Applied Mechanics 66.1 Birkhauser, (1999): 272-273. Print.
• Lancaster, Peter and Renshaw, A. A.. "A stability criterion for parameter-dependent gyroscopic systems". American Society of Mechanical Engineers. Transactions of the ASME. Journal of Applied Mechanics 66.3 Birkhauser, (1999): 660-664. Print.
• Freitas, Pedro and Lancaster, Peter. "On the optimal value of the spectral abscissa for a system of linear oscillators". SIAM Journal on Matrix Analysis and Applications 21.1 Birkhauser, (1999): 195-208 (electronic). Print.
• Guo, Chun and Lancaster, Peter. "Iterative solution of two matrix equations". Mathematics of Computation 68.228 Birkhauser, (1999): 1589-1603. Print.
• Lancaster, Peter. "Strongly stable gyroscopic systems". Electronic Journal of Linear Algebra 5. Birkhauser, (1999): 53-66 (electronic). Print.
• Lancaster, Peter. "On the perturbation of analytic matrix functions". Integral Equations and Operator Theory 34.3 Birkhauser, (1999): 325-338. Print.
• Lancaster, Peter and Zizler, Peter. "On the stability of gyroscopic systems". American Society of Mechanical Engineers. Transactions of the ASME. Journal of Applied Mechanics 65.2 Birkhauser, (1998): 519-522. Print.
• Krupnik, Ilya and Lancaster, Peter. "Linearization, realization, and scalar products for regular matrix polynomials". Linear Algebra and its Applications 272. Birkhauser, (1998): 45-57. Print.
• Krupnik, Ilya and Lancaster, Peter. "{$H$}-selfadjoint and {$H$}-unitary matrix pencils". SIAM Journal on Matrix Analysis and Applications 19.2 Birkhauser, (1998): 307-324 (electronic). Print.
• Krupnik, Ilya and Lancaster, Peter. "Minimal pencil realizations of rational matrix functions with symmetries". Canadian Mathematical Bulletin. Bulletin Canadien de Math\'ematiques 41.2 Birkhauser, (1998): 178-186. Print.
• Guo, Chun and Lancaster, Peter. "Analysis and modification of {N}ewton's method for algebraic {R}iccati equations". Mathematics of Computation 67.223 Birkhauser, (1998): 1089-1105. Print.
• Lancaster, Peter and Zizler, Peter. "The order of neutrality for linear operators on inner product spaces". Linear Algebra and its Applications 259. Birkhauser, (1997): 25-29. Print.
• Dai, Hua and Lancaster, Peter. "Newton's method for a generalized inverse eigenvalue problem". Numerical Linear Algebra with Applications 4.1 Birkhauser, (1997): 1-21. Print.
• Dai, Hua and Lancaster, Peter. "Numerical methods for finding multiple eigenvalues of matrices depending on parameters". Numerische Mathematik 76.2 Birkhauser, (1997): 189-208. Print.
• Hua, Dai and Lancaster, Peter. "Linear matrix equations from an inverse problem of vibration theory". Linear Algebra and its Applications 246. John Wiley & Sons Inc., (1996): 31-47. Print.
• Lancaster, Peter and Matsaev, V.. "Factorization of selfadjoint operator polynomials". Journal of Operator Theory 35.2 John Wiley & Sons Inc., (1996): 337-348. Print.
• Lancaster, Peter and R{\'o}zsa, P.. "The spectrum and stability of a vibrating rail supported by sleepers". Computers & Mathematics with Applications. An International Journal 31.4-5 Birkhauser, (1996): 201-213. Print.
• Krupnik, Ilya, Lancaster, Peter and Zizler, Peter. "Factorization of selfadjoint matrix polynomials with real spectrum". Linear and Multilinear Algebra 40.4 Birkhauser, (1996): 327-336. Print.
• Lancaster, Peter and Rodman, L.. "Minimal symmetric factorizations of symmetric real and complex rational matrix functions". Linear Algebra and its Applications 220. The Clarendon Press Oxford University Press, (1995): 249-282. Print.
• Krupnik, Ilya and Lancaster, Peter. "Factorization of selfadjoint quadratic matrix polynomials with real spectrum". Linear and Multilinear Algebra 39.3 The Clarendon Press Oxford University Press, (1995): 263-272. Print.
• Andrew, A. L., Chu, K. E. and Lancaster, Peter. "On the numerical solution of nonlinear eigenvalue problems". Computing. Archives for Scientific Computing 55.2 The Clarendon Press Oxford University Press, (1995): 91-111. Print.
• Lancaster, Peter and Matsaev, V. I.. "Definitizable operators and quasihyperbolic operator polynomials". Journal of Functional Analysis 131.1 The Clarendon Press Oxford University Press, (1995): 1-28. Print.
• Lancaster, Peter and Ye, Qiang. "Low rank perturbations of strongly definitizable transformations and matrix polynomials". Linear Algebra and its Applications 197/198. The Clarendon Press Oxford University Press, (1994): 3-29. Print.
• Lancaster, Peter and Rodman, L.. "Invariant neutral subspaces for symmetric and skew real matrix pairs". Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 46.3 The Clarendon Press Oxford University Press, (1994): 602-618. Print.
• Lancaster, Peter and Shkalikov, A.. "Damped vibrations of beams and related spectral problems". The Canadian Applied Mathematics Quarterly 2.1 The Clarendon Press Oxford University Press, (1994): 45-90. Print.
• Lancaster, Peter, Shkalikov, A. and Ye, Qiang. "Strongly definitizable linear pencils in {H}ilbert space". Integral Equations and Operator Theory 17.3 The Clarendon Press Oxford University Press, (1993): 338-360. Print.
• Lancaster, Peter and Ye, Qiang. "Definitizable {H}ermitian matrix pencils". Aequationes Mathematicae 46.1-2 (1993): 44-55. Print.
• Lancaster, Peter and Ye, Qiang. "Rayleigh-{R}itz and {L}anczos methods for symmetric matrix pencils". Linear Algebra and its Applications 185. (1993): 173-201. Print.
• Bohl, Erich and Lancaster, Peter. "Perturbation of spectral inverses applied to a boundary layer phenomenon arising in chemical networks". Linear Algebra and its Applications 180. (1993): 35-59. Print.
• Andrew, Alan L., Chu, K. and Lancaster, Peter. "Derivatives of eigenvalues and eigenvectors of matrix functions". SIAM Journal on Matrix Analysis and Applications 14.4 The Clarendon Press Oxford University Press, (1993): 903-926. Print.
• Gohberg, I., Koltracht, I. and Lancaster, Peter. "Second order parallel algorithms for piecewise smooth displacement kernels". Integral Equations and Operator Theory 15.1 (1992): 16-29. Print.
• Barkwell, Lawrence and Lancaster, Peter. "Overdamped and gyroscopic vibrating systems". American Society of Mechanical Engineers. Transactions of the ASME. Journal of Applied Mechanics 59.1 (1992): 176-181. Print.
• Jameson, Antony, Kreindler, Eliezer and Lancaster, Peter. "Symmetric, positive semidefinite, and positive definite real solutions of {$AX=XA\sp {\ssf T}$} and {$AX=YB$}". Linear Algebra and its Applications 160. (1992): 189-215. Print.
• Barkwell, Lawrence and Lancaster, Peter. "Gyroscopically stabilized systems: a class of quadratic eigenvalue problems with real spectrum". Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 44.1 (1992): 42-53. Print.
• Andrew, Alan L., Chu, K. and Lancaster, Peter. "Sensitivities of eigenvalues and eigenvectors of problems nonlinear in the eigenparameter". Applied Mathematics Letters. An International Journal of Rapid Publication 5.3 (1992): 69-72. Print.
• Farid, F. O. and Lancaster, Peter. "Spectral Properties of Diagonally Dominant Infinite Matrices. II". Linear Algebra and its Applications 143. Springer, (1991): 7-17. Print.
• Bruckstein, Alfred, Kailath, Thomas, Koltracht, Israel and Lancaster, Peter. "On the reconstruction of layered media from reflection data". SIAM Journal on Matrix Analysis and Applications 12.1 Springer, (1991): 24-40. Print.
• Lancaster, Peter and Ye, Qiang. "Variational and numerical methods for symmetric matrix pencils". Bulletin of the Australian Mathematical Society 43.1 Springer, (1991): 1-17. Print.
• Elsner, L., Koltracht, I. and Lancaster, Peter. "Convergence properties of {ART} and {SOR} algorithms". Numerische Mathematik 59.1 Springer, (1991): 91-106. Print.
• Koltracht, Israel, Lancaster, Peter and Smith, Digby. "The structure of some matrices arising in tomography". Linear Algebra and its Applications 130. Springer, (1990): 193-218. Print.
• Koltracht, I. and Lancaster, Peter. "Constraining strategies for linear iterative processes". IMA Journal of Numerical Analysis 10.4 Springer, (1990): 555-567. Print.
• Gohberg, I., Koltracht, I. and Lancaster, Peter. "On the numerical solution of integral equations with piecewise continuous displacement kernels". Integral Equations and Operator Theory 12.4 Birkhauser, (1989): 511-538. Print.
• Farid, F. O. and Lancaster, Peter. "Spectral Properties of Diagonally Dominant Infinite Matrices, Part I.". Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 111A.3-4 Birkhauser, (1989): 301-314. Print.
• Gohberg, I., Kaashoek, M. A. and Lancaster, Peter. "General theory of regular matrix polynomials and band {T}oeplitz operators". Integral Equations and Operator Theory 11.6 Birkhauser, (1988): 776-882. Print.
• Lancaster, Peter and Ye, Qiang. "Inverse spectral problems for linear and quadratic matrix pencils". Linear Algebra and its Applications 107. Birkhauser, (1988): 293-309. Print.
• Koltracht, I. and Lancaster, Peter. "Generalized {S}chur parameters and the effects of perturbations". Linear Algebra and its Applications 105. Birkhauser, (1988): 109-129. Print.
• Lancaster, Peter and Maroulas, J.. "Selective perturbation of spectral properties of vibrating systems using feedback". Linear Algebra and its Applications 98. Birkhauser, (1988): 309-330. Print.
• Gohberg, I., Koltracht, I. and Lancaster, Peter. "Second order parallel algorithms for {F}redholm integral equations with continuous displacement kernels". Integral Equations and Operator Theory 10.4 Birkhauser, (1987): 577-594. Print.
• Lancaster, Peter and Maroulas, J.. "Inverse eigenvalue problems for damped vibrating systems". Journal of Mathematical Analysis and Applications 123.1 Birkhauser, (1987): 238-261. Print.
• Lancaster, Peter. "Alexander {M}. {O}strowski, 1893-1986". Aequationes Mathematicae 33.2-3 Birkhauser, (1987): 121-122. Print.
• Gohberg, I., Kailath, T., Koltracht, I. and Lancaster, Peter. "Linear complexity parallel algorithms for linear systems of equations with recursive structure". Linear Algebra and its Applications 88/89. Birkhauser, (1987): 271-315. Print.
• Lancaster, Peter, Ran, A. C. M. and Rodman, L.. "An existence and monotonicity theorem for the discrete algebraic matrix {R}iccati equation". Linear and Multilinear Algebra 20.4 Birkhauser, (1987): 353-361. Print.
• Koltracht, I. and Lancaster, Peter. "A definiteness test for {H}ankel matrices and their lower submatrices". Computing. Archives for Scientific Computing 39.1 Birkhauser, (1987): 19-26. Print.
• Lancaster, Peter. "Common eigenvalues, divisors, and multiples of matrix polynomials: a review". Linear Algebra and its Applications 84. John Wiley & Sons Inc., (1986): 139-160. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. "On {H}ermitian solutions of the symmetric algebraic {R}iccati equation". SIAM Journal on Control and Optimization 24.6 John Wiley & Sons Inc., (1986): 1323-1334. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. "Quadratic matrix polynomials with a parameter". Advances in Applied Mathematics 7.3 John Wiley & Sons Inc., (1986): 253-281. Print.
• Lancaster, Peter, Ran, A. C. M. and Rodman, L.. "Hermitian solutions of the discrete algebraic {R}iccati equation". International Journal of Control 44.3 John Wiley & Sons Inc., (1986): 777-802. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. "Perturbation of analytic {H}ermitian matrix functions". Applicable Analysis. An International Journal 20.1-2 John Wiley & Sons Inc., (1985): 23-48. Print.
• Elsner, L. and Lancaster, Peter. "The spectral variation of pencils of matrices". Journal of Computational Mathematics. An International Journal on Numerical Methods, Analysis and Applications 3.3 John Wiley & Sons Inc., (1985): 262-274. Print.
• Lancaster, Peter and Maroulas, J.. "The kernel of the {B}ezoutian for operator polynomials". Linear and Multilinear Algebra 17.3-4 John Wiley & Sons Inc., (1985): 181-201. Print.
• Lancaster, Peter, Lerer, L. and Tismenetsky, M.. "Factored forms for solutions of {$AX-XB=C$} and {$X-AXB=C$} in companion matrices". Linear Algebra and its Applications 62. Springer, (1984): 19-49. Print.
• Lancaster, Peter and R{\'o}zsa, P.. "Eigenvectors of {$H$}-selfadjoint matrices". Zeitschrift f\"ur Angewandte Mathematik und Mechanik. Ingenieurwissenschaftliche Forschungsarbeiten 64.9 Springer, (1984): 439-441. Print.
• Gohberg, Israel, Lancaster, Peter and Rodman, Leiba. "A sign characteristic for selfadjoint meromorphic matrix functions". Applicable Analysis. An International Journal 16.3 Birkhauser Verlag, (1983): 165-185. Print.
• Lancaster, Peter and Tismenetsky, M.. "Inertia characteristics of selfadjoint matrix polynomials". Linear Algebra and its Applications 52/53. Birkhauser Verlag, (1983): 479-496. Print.
• Lancaster, Peter and R{\'o}zsa, P.. "On the matrix equation {$AX+X\sp{\ast} A\sp{\ast} =C$}". Society for Industrial and Applied Mathematics. Journal on Algebraic and Discrete Methods 4.4 Birkhauser Verlag, (1983): 432-436. Print.
• Lancaster, Peter and Tismenetsky, M.. "Some extensions and modifications of classical stability tests for polynomials". International Journal of Control 38.2 Birkhauser Verlag, (1983): 369-380. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. "Perturbations of {$H$}-selfadjoint matrices, with applications to differential equations". Integral Equations and Operator Theory 5.5 Hemisphere, (1982): 718-757. Print.
• Lancaster, Peter and Pattabhiraman, M. V.. "The local determination of {J}ordan bases for {$H$}-selfadjoint operators". Linear Algebra and its Applications 48. Dekker, (1982): 191-199. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. "Factorization of selfadjoint matrix polynomials with constant signature". Linear and Multilinear Algebra 11.3 Academic Press Inc. [Harcourt Brace Jovanovich Publishers], (1982): 209-224. Print.
• Lancaster, Peter and Salkauskas, Kes. "Surfaces generated by moving least squares methods". Mathematics of Computation 37.155 Academic Press Inc. [Harcourt Brace Jovanovich Publishers], (1981): 141-158. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. "Spectral analysis of selfadjoint matrix polynomials". Annals of Mathematics. Second Series 112.1 Academic Press Inc. [Harcourt Brace Jovanovich Publishers], (1980): 33-71. Print.
• Barnett, S. and Lancaster, Peter. "Some properties of the {B}ezoutian for polynomial matrices". Linear and Multilinear Algebra 9.2 Academic Press Inc. [Harcourt Brace Jovanovich Publishers], (1980): 99-110. Print.
• Lancaster, Peter and Rodman, L.. "Existence and uniqueness theorems for the algebraic {R}iccati equation". International Journal of Control 32.2 Academic Press Inc. [Harcourt Brace Jovanovich Publishers], (1980): 285-309. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. "On selfadjoint matrix polynomials". Integral Equations and Operator Theory 2.3 Academic Press Inc. [Harcourt Brace Jovanovich Publishers], (1979): 434-439. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. "Perturbation theory for divisors of operator polynomials". SIAM Journal on Mathematical Analysis 10.6 Academic Press Inc. [Harcourt Brace Jovanovich Publishers], (1979): 1161-1183. Print.
• Lancaster, Peter. "Solving quadratic equations". Menemui Matematik. (Discovering Mathematics) 1.3 Academic Press Inc. [Harcourt Brace Jovanovich Publishers], (1979): 23-36. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. "Representations and divisibility of operator polynomials". Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 30.5 (1978): 1045-1069. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. "Spectral analysis of matrix polynomials. {I}. {C}anonical forms and divisors". Linear Algebra and Appl. 20.1 (1978): 1-44. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. "Spectral analysis of matrix polynomials. {II}. {T}he resolvent form and spectral divisors". Linear Algebra and Appl. 21.1 (1978): 65-88. Print.
• Lancaster, Peter and Rokne, Jon G.. "Solutions of nonlinear operator equations". SIAM Journal on Mathematical Analysis 8.3 Birkhauser, (1977): 448-457. Print.
• Terray, J. and Lancaster, Peter. "On the numerical calculation of eigenvalues and eigenvectors of operator polynomials". J. Math. Anal. Appl. 60.2 (1977): 370-378. Print.
• Lancaster, Peter. "A fundamental theorem on lambda-matrices with applications. {II}. {D}ifference equations with constant coefficients". Linear Algebra and Appl. 18.3 Birkhauser, (1977): 213-222. Print.
• Lancaster, Peter. "A fundamental theorem on lambda-matrices with applications. {I}. {O}rdinary differential equations with constant coefficients". Linear Algebra and Appl. 18.3 Birkhauser, (1977): 189-211. Print.
• Watkins, D. S. and Lancaster, Peter. "Some families of finite elements". J. Inst. Math. Appl. 19.4 Birkhauser, (1977): 385-397. Print.
• Lancaster, Peter. "Interpolation in a rectangle and finite elements of high degree". J. Inst. Math. Appl. 18.1 Birkhauser, (1976): 67-77. Print.
• Lancaster, Peter and Wimmer, Harald K.. "Zur {T}heorie der {$\lambda$}-{M}atrizen". Mathematische Nachrichten 68. Birkhauser, (1975): 325-330. Print.
• Schmidt, Eckard, Lancaster, Peter and Watkins, David. "Bases of splines associated with constant coefficient differential operators". SIAM Journal on Numerical Analysis 12.4 Birkhauser, (1975): 630-645. Print.
• Cross, G. W. and Lancaster, Peter. "Square roots of complex matrices". Linear and Multilinear Algebra 1. Birkhauser, (1973/74): 289-293. Print.
• Lancaster, Peter and Farahat, Hanafi K.. "Norms on direct sums and tensor products". Mathematics of Computation 26. Birkhauser, (1972): 401-414. Print.
• Lancaster, Peter. "A note on sub-multiplicative norms". Numerische Mathematik 19. Birkhauser, (1972): 206-208. Print.
• Schmidt, Eckard and Lancaster, Peter. "{$L$}-splines for constant coefficient differential operators". , Birkhauser, (1971): 457-462. Print.
• Lancaster, Peter. "Some questions in the classical theory of vibrating systems". Bul. Inst. Politehn. Ia\c si (N.S.) 17(21).1-2, part 1 Birkhauser, (1971): 125-132. Print.
• Lancaster, Peter. "Jordan chains for lambda matrices. {II}". Aequationes Mathematicae 5. Birkhauser, (1970): 290-293. Print.
• Lancaster, Peter. "Explicit solutions of linear matrix equations". SIAM Review. A Publication of the Society for Industrial and Applied Mathematics 12. Birkhauser, (1970): 544-566. Print.
• Pattabhiraman, M. V. and Lancaster, Peter. "Spectral properties of a polynomial operator". Numerische Mathematik 13. Birkhauser, (1969): 247-259. Print.
• Rokne, J. and Lancaster, Peter. "Automatic errorbounds for the approximate solution of equations". Computing (Arch. Elektron. Rechnen) 4. Birkhauser, (1969): 294-303. Print.
• Lancaster, Peter and Webber, P. N.. "Jordan chains for lambda matrices". Linear Algebra and Appl. 1. Academic Press, (1968): 563-569. Print.
• Lancaster, Peter. "Error analysis for the {N}ewton-{R}aphson method". Numerische Mathematik 9. Academic Press, (1966): 55-68. Print.
• Lancaster, Peter. "Convergence of the {N}ewton-{R}aphson method for arbitrary polynomials". Math. Gaz. 48. Academic Press, (1964): 291-295. Print.
• Lancaster, Peter. "Bounds for latent roots in damped vibration problems". SIAM Review. A Publication of the Society for Industrial and Applied Mathematics 6. Academic Press, (1964): 121-125. Print.
• Lancaster, Peter. "On eigenvalues of matrices dependent on a parameter". Numerische Mathematik 6. Academic Press, (1964): 377-387. Print.
• Lancaster, Peter. "Algorithms for lambda-matrices". Numerische Mathematik 6. Academic Press, (1964): 388-394. Print.
• Lancaster, Peter. "Some applications of the {N}ewton-{R}aphson method to non-linear matrix problems". Proc. Roy. Soc. Ser. A 271. (1963): 324-331. Print.
• Lancaster, Peter. "On regular pencils of matrices arising in the theory of vibrations". Quart. J. Mech. Appl. Math. 16. (1963): 253-257. Print.
• Lancaster, Peter. "A generalized {R}ayleigh quotient iteration for lambda-matrices". Archive for Rational Mechanics and Analysis 8. (1961): 309-322. Print.
• Lancaster, Peter. "Free vibrations of lightly damped systems by perturbations methods.". Quart. J. Mech. Appl. Math. 13. (1960): 138-155. Print.
• Lancaster, Peter. "Inversion of lambda-matrices and application to the theory of linear vibrations". Archive for Rational Mechanics and Analysis 6. (1960): 105-114. Print.

Preprint

• Lancaster, Peter. "Lectures on Linear Algebra, Control, and Stability". , (1998). Print.