Zobrazeno 1 - 10
of 13
pro vyhledávání: '"Zvonimir Bujanović"'
The Schur decomposition of a square matrix $A$ is an important intermediate step of state-of-the-art numerical algorithms for addressing eigenvalue problems, matrix functions, and matrix equations. This work is concerned with the following task: Comp
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a546820ab14a653c5db34aba229f5f5b
https://www.bib.irb.hr/1196442
https://www.bib.irb.hr/1196442
Autor:
Zvonimir Bujanović, Daniel Kressner
A few matrix-vector multiplications with random vectors are often sufficient to obtain reasonably good estimates for the norm of a general matrix or the trace of a symmetric positive semi-definite matrix. Several such probabilistic estimators have be
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8c2731d0e73a1abb3b3ab7415eea3a25
http://arxiv.org/abs/2004.06433
http://arxiv.org/abs/2004.06433
Publikováno v:
Numerische Mathematik
In recent years, several new approaches for solving the large-scale continuous-time algebraic Riccati equation have appeared in the literature. Amodei and Buchot suggest computing a low-dimensional invariant subspace of the associated Hamiltonian mat
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1da331ee2aa86bbda2998fea0cd09148
https://doi.org/10.1007/s00211-017-0907-5
https://doi.org/10.1007/s00211-017-0907-5
Autor:
Zvonimir Bujanović, Peter Benner
Publikováno v:
Linear Algebra and its Applications. 488:430-459
This article discusses an approach to solving large-scale algebraic Riccati equations (AREs) by computing a low-dimensional stable invariant subspace of the associated Hamiltonian matrix. We give conditions on AREs to admit solutions of low numerical
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2d859d358921574dca98a9b2b7c9d0a3
https://doi.org/10.1016/j.laa.2015.09.027
https://doi.org/10.1016/j.laa.2015.09.027
Publikováno v:
SIAM Journal on Scientific Computing
In this paper, we discuss numerical methods for solving large-scale continuous-time algebraic Riccati equations. These methods have been the focus of intensive research in recent years, and significant progress has been made in both the theoretical u
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cdb339a08f7b7d3824cfa7af77a09535
http://arxiv.org/abs/1811.00850
http://arxiv.org/abs/1811.00850
This paper proposes a combination of a hybrid CPU--GPU and a pure GPU software implementation of a direct algorithm for solving shifted linear systems $(A-\sigma I)X=B$ with a large number of complex shifts $\sigma$ and multiple right-hand sides. Suc
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e49cdba005939741409f52190be1434e
https://doi.org/10.1137/17m1144465
https://doi.org/10.1137/17m1144465
Autor:
Zlatko Drmač, Zvonimir Bujanović
Publikováno v:
Numerical Linear Algebra with Applications. 22:220-232
Summary This paper introduces a new framework for implicit restarting of the Krylov–Schur algorithm. It is shown that restarting with arbitrary polynomial filter is possible by reassigning some of the eigenvalues of the Rayleigh quotient through a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2e05125428582a96da770dc63aa539ef
https://doi.org/10.1002/nla.1944
https://doi.org/10.1002/nla.1944
Autor:
Zvonimir Bujanović
Publikováno v:
Linear Algebra and its Applications. 438:4606-4624
This article discusses Ritz and harmonic Ritz values computed from a Krylov subspace, generated by a normal matrix. We give necessary and sufficient conditions for a given tuple of complex numbers to represent Ritz values: the existence of a positive
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::78e5da9ccf576ed472bc7944c7d396db
https://doi.org/10.1016/j.laa.2013.02.014
https://doi.org/10.1016/j.laa.2013.02.014
Autor:
Daniel Kressner, Zvonimir Bujanović
Any symmetric matrix can be reduced to antitriangular form in finitely many steps by orthogonal similarity transformations. This form reveals the inertia of the matrix and has found applications in, e.g., model predictive control and constraint preco
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::11607b3bbe3d48b7fc95537b6ebbbf82
https://www.bib.irb.hr/762106
https://www.bib.irb.hr/762106
Autor:
Zvonimir Bujanović, Zlatko Drmač
Publikováno v:
ACM Transactions on Mathematical Software. 35:1-28
This article reports an unexpected and rather erratic behavior of the LAPACK software implementation of the QR factorization with Businger-Golub column pivoting. It is shown that, due to finite precision arithmetic, the software implementation of the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::451914d5aea3dcf9a4372632d724cd6a
https://doi.org/10.1145/1377612.1377616
https://doi.org/10.1145/1377612.1377616