28 citations · 164 across the 19 of their papers we have counts for
21 papers
What Drives AI Citations? Content, Retrieval and Model Knowledge in Generative Engine Optimization (GEO)
Mahe Chen, Nick Koudas
Generative search engines such as ChatGPT, Gemini and Perplexity now decide which Web pages users see as sources, and a growing industry of generative engine optimization advises p…
Computing leaky waves in semi-analytical waveguide models by exponential residual relaxation
Hauke Gravenkamp, Bor Plestenjak, Daniel A. Kiefer
Semi-analytical methods for the modeling of guided waves in structures of constant cross-section lead to frequency-dependent polynomial eigenvalue problems for the wavenumbers and…
A Sylvester equation approach for the computation of zero-group-velocity points in waveguides
Bor Plestenjak, Daniel A. Kiefer, Hauke Gravenkamp
Eigenvalues of parameter-dependent quadratic eigenvalue problems form eigencurves. The critical points on these curves, where the derivative vanishes, are of practical interest. A…
On properties and numerical computation of critical points of eigencurves of bivariate matrix pencils
Bor Plestenjak
We investigate critical points of eigencurves of bivariate matrix pencils . Points for which form algebraic curves in and we focus…
Randomized methods for computing joint eigenvalues, with applications to multiparameter eigenvalue problems and root finding
Haoze He, Daniel Kressner, Bor Plestenjak
It is well known that a family of commuting matrices can be simultaneously triangularized by a unitary similarity transformation. The diagonal entries of the triangular…
Solving singular generalized eigenvalue problems. Part III: structure preservation
Michiel E. Hochstenbach, Christian Mehl, Bor Plestenjak
In Parts I and II of this series of papers, three new methods for the computation of eigenvalues of singular pencils were developed: rank-completing perturbations, rank-projections…
Numerical methods for eigenvalues of singular polynomial eigenvalue problems
Michiel E. Hochstenbach, Christian Mehl, Bor Plestenjak
Recently, three numerical methods for the computation of eigenvalues of singular matrix pencils, based on a rank-completing perturbation, a rank-projection, or an augmentation were…
Computation of leaky waves in layered structures coupled to unbounded media by exploiting multiparameter eigenvalue problems
Hauke Gravenkamp, Bor Plestenjak, Daniel A. Kiefer +1
We present a semi-analytical approach to compute quasi-guided elastic wave modes in horizontally layered structures radiating into unbounded fluid or solid media. This problem is o…
Notes on osculations and mode tracing in semi-analytical waveguide modeling
Hauke Gravenkamp, Bor Plestenjak, Daniel A. Kiefer
The dispersion curves of (elastic) waveguides frequently exhibit crossings and osculations (also known as veering, repulsion, or avoided crossing). Osculations are regions in the d…
Analysis of eigenvalue condition numbers for a class of randomized numerical methods for singular matrix pencils
Daniel Kressner, Bor Plestenjak
The numerical solution of the generalized eigenvalue problem for a singular matrix pencil is challenging due to the discontinuity of its eigenvalues. Classically, such problems are…
Numerical methods for rectangular multiparameter eigenvalue problems, with applications to finding optimal ARMA and LTI models
Michiel E. Hochstenbach, Tomaž Košir, Bor Plestenjak
Standard multiparameter eigenvalue problems (MEPs) are systems of linear -parameter square matrix pencils. Recently, a new form of multiparameter eigenvalue problems ha…
Computing zero-group-velocity points in anisotropic elastic waveguides: Globally and locally convergent methods
Daniel A. Kiefer, Bor Plestenjak, Hauke Gravenkamp +1
Dispersion curves of elastic waveguides exhibit points where the group velocity vanishes while the wavenumber remains finite. These are the so-called zero-group-velocity (ZGV) poin…
Solving singular generalized eigenvalue problems. Part II: projection and augmentation
Michiel E. Hochstenbach, Christian Mehl, Bor Plestenjak
Generalized eigenvalue problems involving a singular pencil may be very challenging to solve, both with respect to accuracy and efficiency. While Part I presented a rank-completing…
On the singular two-parameter eigenvalue problem II
Tomaž Košir, Bor Plestenjak
In the 1960s, Atkinson introduced an abstract algebraic setting for multiparameter eigenvalue problems. He showed that a nonsingular multiparameter eigenvalue problem is equivalent…
Computing several eigenvalues of nonlinear eigenvalue problems by selection
Michiel E. Hochstenbach, Bor Plestenjak
Computing more than one eigenvalue for (large sparse) one-parameter polynomial and general nonlinear eigenproblems, as well as for multiparameter linear and nonlinear eigenproblems…
Solving singular generalized eigenvalue problems by a rank-completing perturbation
Michiel E. Hochstenbach, Christian Mehl, Bor Plestenjak
Generalized eigenvalue problems involving a singular pencil are very challenging to solve, both with respect to accuracy and efficiency. The existing package Guptri is very elegant…
Subspace Methods for 3-Parameter Eigenvalue Problems
Michiel E. Hochstenbach, Karl Meerbergen, Emre Mengi +1
We propose subspace methods for 3-parameter eigenvalue problems. Such problems arise when separation of variables is applied to separable boundary value problems; a particular exam…
Simple determinantal representations of up to quintic bivariate polynomials
Anita Buckley, Bor Plestenjak
For bivariate polynomials of degree we give fast numerical constructions of determinantal representations with matrices. Unlike some other available constructi…
Uniform determinantal representations
Ada Boralevi, Jasper van Doornmalen, Jan Draisma +2
The problem of expressing a specific polynomial as the determinant of a square matrix of affine-linear forms arises from algebraic geometry, optimisation, complexity theory, and sc…
Minimal determinantal representations of bivariate polynomials
Bor Plestenjak
For a square-free bivariate polynomial of degree we introduce a simple and fast numerical algorithm for the construction of matrices , , and such that…
Roots of bivariate polynomial systems via determinantal representations
Bor Plestenjak, Michiel E. Hochstenbach
We give two determinantal representations for a bivariate polynomial. They may be used to compute the zeros of a system of two of these polynomials via the eigenvalues of a two-par…