Zobrazeno 1 - 10
of 136
pro vyhledávání: '"Plestenjak, Bor"'
Publikováno v:
Numerical Algorithms (2024)
It is well known that a family of $n\times n$ commuting matrices can be simultaneously triangularized by a unitary similarity transformation. The diagonal entries of the triangular matrices define the $n$ joint eigenvalues of the family. In this work
Externí odkaz:
http://arxiv.org/abs/2409.00500
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 developed. We show that all three approaches can be generalized to tr
Externí odkaz:
http://arxiv.org/abs/2406.16832
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, and augmentation. It was observed that a straightforward structure-p
Externí odkaz:
http://arxiv.org/abs/2406.07109
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 of relevance, e.g., for the simulation of guided ultrasound in embedded
Externí odkaz:
http://arxiv.org/abs/2404.15277
Publikováno v:
Ultrasonics, vol. 135, p. 107112, 2023
The dispersion curves of (elastic) waveguides frequently exhibit crossings and osculations (also known as veering, repulsion, or avoided crossing). Osculations are regions in the dispersion diagram where curves approach each other arbitrarily closely
Externí odkaz:
http://arxiv.org/abs/2310.06086
Autor:
Kressner, Daniel, Plestenjak, Bor
Publikováno v:
BIT Numer. Math. 64, 32 (2024)
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 addressed by first extracting the regular part through the staircase
Externí odkaz:
http://arxiv.org/abs/2305.13118
Publikováno v:
Numer. Linear Algebra Appl. (2023) e2450
Standard multiparameter eigenvalue problems (MEPs) are systems of $k\ge 2$ linear $k$-parameter square matrix pencils. Recently, a new form of multiparameter eigenvalue problems has emerged: a rectangular MEP (RMEP) with only one multivariate rectang
Externí odkaz:
http://arxiv.org/abs/2212.01867
Publikováno v:
The Journal of the Acoustical Society of America, vol. 153, no. 2, pp. 1386-1398, Feb. 2023
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) points. As the elastodynamic energy at these points remains confined close
Externí odkaz:
http://arxiv.org/abs/2211.01995
Publikováno v:
SIAM Journal on Matrix Analysis and Applications 44 (2023) 1589-1618
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 addition to a singular pencil, we now develop two alternative methods
Externí odkaz:
http://arxiv.org/abs/2208.01359
Publikováno v:
In Journal of Sound and Vibration 5 February 2025 596
