Bor Plestenjak

Software:

• MultiParEig – MATLAB toolbox for multiparameter eigenvalue problems
• BiRoots – MATLAB toolbox for roots of bivariate polynomial systems
• MCTlink - extends MATLink with two new commands for writing and retrieving matrices using MP format in Matlab by Advanpix Multiprecision Computing Toolbox.

Submitted:

• B. Plestenjak, D.A. Kiefer, H. Gravenkamp: A Sylvester equation approach for the computation of zero-group-velocity points in waveguides, arXiv 2411.09584.
• B. Plestenjak: On properties and numerical computation of critical points of eigencurves of bivariate matrix pencils, arXiv 2411.07450.
• M.E. Hochstenbach, C. Mehl, B. Plestenjak: Solving singular generalized eigenvalue problems part III: structure preservation, arXiv 2406.07109.

Published papers:

• M.E. Hochstenbach, C. Mehl, B. Plestenjak: Numerical methods for eigenvalues of singular polynomial eigenvalue problems, Linear Algebra Appl. 719 (2025) 1-33,(arXiv).
• H. He, D. Kressner, B. Plestenjak: Randomized methods for computing joint eigenvalues, with applications to multiparameter eigenvalue problems and root finding, Numer. Algor. (2024), (arXiv)
• H. Gravenkamp, B. Plestenjak, D.A. Kiefer, E. Jarlebring: Computation of leaky waves in layered structures coupled to unbounded media by exploiting multiparameter eigenvalue problems, J. Sound Vib. 596 (2025) 118716, (arXiv)
• D. Kressner, B. Plestenjak: Analysis of a class of randomized numerical methods for singular matrix pencils, BIT Numer. Math. 64 (2024), (arXiv).
• M.E. Hochstenbach, T. Košir, B. Plestenjak: Numerical methods for rectangular multiparameter eigenvalue problems, with applications to finding optimal ARMA and LTI models, Numer. Linear Algebra Appl. 31 (2024) e2540, (arXiv).
• M.E. Hochstenbach, C. Mehl, B. Plestenjak: Solving singular generalized eigenvalue problems part II: projection and augmentation, SIAM J. Matrix Anal. Appl. 44 (2023) 1589-1618, (arXiv).
• H. Gravenkamp, B. Plestenjak, D.A. Kiefer: Notes on osculations and mode tracing in semi-analytical waveguide modeling, Ultrasonics 135 (2023) 107112, (arXiv).
• D.A. Kiefer, B. Plestenjak, H. Gravenkamp, C. Prada: Computing zero-group-velocity points in anisotropic elastic waveguides: globally and locally convergent methods, J. Acoust. Soc. Am. 153 (2023) 1386-1398, (arXiv).
• T. Košir, B. Plestenjak: On the singular two-parameter eigenvalue problem II, Linear Algebra Appl. 649 (2022) 433-451, (arXiv).
• M.E. Hochstenbach, B. Plestenjak, Computing several eigenvalues of nonlinear eigenvalue problems by selection, Calcolo 57 (2020) 16, (arXiv).
• M.E. Hochstenbach, C. Mehl, B. Plestenjak, Solving singular generalized eigenvalue problems by a rank-completing perturbation, SIAM J. Matrix Anal. Appl. 40 (2019) 1022-1046 (arXiv).
• M.E. Hochstenbach, K. Meerbergen, E. Mengi, B. Plestenjak, Subspace methods for 3-parameter eigenvalue problems, Numer. Linear Algebra Appl. 26 (2019) e2240 (arXiv).
• A. Buckley, B. Plestenjak: Simple determinantal representations of up to quintic bivariate polynomials, Linear and Multilinear Algebra 66 (2018) 2266-2285 (arXiv).
• A. Boralevi, J. van Doornmalen, J. Draisma, M. E. Hochstenbach, B. Plestenjak: Uniform determinantal representations, SIAM J. Appl. Algebra Geometry 1 (2017) 415-441 (arXiv).
• B. Plestenjak: Minimal determinantal representations of bivariate polynomials, Linear Algebra Appl. 532 (2017) 550-569 (arXiv).
• B. Plestenjak, M. E. Hochstenbach: Roots of bivariate polynomial systems via determinantal representations, SIAM J. Sci. Comput. 38 (2016) A765-A788 (arXiv).
• B. Plestenjak: Numerical methods for nonlinear two-parameter eigenvalue problems, BIT Numer. Math. 56 (2016) 241-262 (preprint).
• K. Meerbergen, B. Plestenjak: A Sylvester-Arnoldi type method for the generalized eigenvalue problem with two-by-two operator determinants, Numer. Linear Algebra Appl. 22 (2015) 1131-1146 (preprint).
• B. Plestenjak, C. I. Gheorghiu, M. E. Hochstenbach: Spectral collocation for multiparameter eigenvalue problems arising from separable boundary value problems, J. Comput. Phys. 298 (2015) 585-601 (preprint)
• M. E. Hochstenbach, A. Muhič, B. Plestenjak: Jacobi-Davidson methods for polynomial two-parameter eigenvalue problems, J. Comput. Appl. Math. 288 (2015) 251-263 (preprint)
• A. Muhič, B. Plestenjak: A method for computing all values λ such that A + λB has a multiple eigenvalue, Linear Algebra Appl. 440 (2014) 345-359 (preprint)
• C. I. Gheorghiu, M. E. Hochstenbach, B. Plestenjak, J. Rommes: Spectral collocation solutions to multiparameter Mathieu’s system, Appl. Math. Comput. 218 (2012) 11990-12000 (preprint)
• M. E. Hochstenbach, A. Muhič, B. Plestenjak: On linearizations of the quadratic two-parameter eigenvalue problems, Linear Algebra Appl. 436 (2012) 2725-2743 (preprint)
• A. Muhič, B. Plestenjak: On the quadratic two-parameter eigenvalue problem and its linearization, Linear Algebra Appl. 432 (2010) 2529-2542 (preprint)
• A. Muhič, B. Plestenjak: On the singular two-parameter eigenvalue problem, Electron. J. Linear Algebra 18 (2009) 420-437.
• M. E. Hochstenbach, B. Plestenjak: Harmonic Rayleigh-Ritz for the multiparameter eigenvalue problem, Electron. Trans. Numer. Anal. 29 (2008) 81-96.
• B. Plestenjak, M. Van Barel, E. Van Camp: A Cholesky LR algorithm for the positive definite symmetric diagonal-plus-semiseparable eigenproblem, Linear Algebra Appl. 428 (2008) 586-599 (preprint) (Fortran 77 implementation of the algorithm) (Matlab implementation of the algorithm)
• B. Plestenjak, Numerical methods for the tridiagonal hyperbolic quadratic eigenvalue problem, SIAM J. Matrix Anal. Appl. 28 (2006) 1157-1172 (preprint) (Fortran 95 implementation of the algorithm)
• M. E. Hochstenbach, T. Košir, B. Plestenjak: A Jacobi-Davidson type method for the two-parameter eigenvalue problem, SIAM J. Matrix Anal. Appl. 26 (2005) 477-497 (preprint) (Matlab implementation of the algorithm is available on e-mail request)
• M. E. Hochstenbach, B. Plestenjak: Backward error, condition numbers, and pseudospectrum for the multiparameter eigenvalue problem, Linear Algebra Appl. 375 (2003) 63-81 (preprint)
• M. E. Hochstenbach, B. Plestenjak: A Jacobi-Davidson type method for a right definite two-parameter eigenvalue problem, SIAM J. Matrix Anal. Appl. 24 (2002) 392-410 (preprint) (Matlab implementation of the algorithm is available on e-mail request)
• T. Bhattacharyya, T. Košir, B. Plestenjak: Right Definite Multiparameter Sturm-Liouville Problems with Eigenparameter Dependent Boundary Conditions, Proc. Edinb. Math. Soc. 45 (2002) 565-578 (preprint)
• T. Košir, B. Plestenjak: On the stability of invariant subspaces of commuting matrices, Linear Algebra Appl. 342 (2002) 133-147 (preprint)
• B. Plestenjak: A Continuation Method for A Weakly Elliptic Two-Parameter Eigenvalue Problem, IMA J. Num. Anal. 21 (2001) 199-216 (preprint)
• B. Plestenjak: A Continuation Method for A Right Definite Two-Parameter Eigenvalue Problem, SIAM J. Matrix Anal. Appl. 21 (2000) 1163-1184 (preprint)
• B. Plestenjak: An Algorithm for Drawing Planar Graphs, Softw. Pract. Exper. 29 (1999) 973-984 (preprint)
• B. Plestenjak: A numerical algorithm for computing a basis for the root subspace at a nonderogatory eigenvalue of a multiparameter system, Linear Algebra Appl. 285 (1998) 257-276.
• B. Plestenjak, T. Pisanski, A. Graovac: Generating Fullerenes at Random, J. Chem. Inf. Comput. Sci. 36 (1996) 825-828 (preprint)
• B. Plestenjak, T. Pisanski, A. Graovac: The minimal non-fullerene Voronoi polyhedra, Match 33 (1996) 157-168 (preprint)
• T. Pisanski, B. Plestenjak, A. Graovac: NiceGraph Program and its Applications in Chemistry, Croat. Chem. Acta 68 (1995) 283-292 (preprint)

Proceedings:

• V. Batagelj, B. Plestenjak: Optimal arrangements of n points on a sphere and in a circle, SOR' 01 Proceedings (Preddvor) 83-87, Slov. Soc. Inform., Ljubljana 2001.