Zobrazeno 1 - 10
of 147
pro vyhledávání: '"Marc Van Barel"'
Publikováno v:
Entropy, Vol 18, Iss 5, p 182 (2016)
Spectral clustering methods allow datasets to be partitioned into clusters by mapping the input datapoints into the space spanned by the eigenvectors of the Laplacian matrix. In this article, we make use of the incomplete Cholesky decomposition (ICD)
Externí odkaz:
https://doaj.org/article/216b0c2656974ea1aa4210c3bcb3f05c
The general properties and mathematical structures of semiseparable matrices were presented in volume 1 of Matrix Computations and Semiseparable Matrices. In volume 2, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi discuss the theory of struct
In recent years several new classes of matrices have been discovered and their structure exploited to design fast and accurate algorithms. In this new reference work, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi present the first comprehensi
Many problems in Science and Engineering give rise to linear integral equations of the first kind with a smooth kernel. Discretization of the integral operator yields a matrix, whose singular values cluster at the origin. We describe the approximatio
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e24c23a15fe408252a8e97a446c0f65a
http://arxiv.org/abs/2204.05740
http://arxiv.org/abs/2204.05740
Publikováno v:
Special Matrices, Vol 8, Iss 1, Pp 144-159 (2020)
An important decomposition for unitary matrices, the CMV-decomposition, is extended to general non-unitary matrices. This relates to short recurrence relations constructing biorthogonal bases for a particular pair of extended Krylov subspaces.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b70c97526e52bebff49c031873fdda5a
https://doi.org/10.1515/spma-2020-0107
https://doi.org/10.1515/spma-2020-0107
Autor:
Niel Van Buggenhout, Marc Van Barel
Publikováno v:
BIT Numerical Mathematics. 62:1091-1092
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ff9129759e350b0e0b69fb4a5985aacd
https://doi.org/10.1007/s10543-022-00921-3
https://doi.org/10.1007/s10543-022-00921-3
Autor:
Françoise Tisseur, Marc Van Barel
A new measure called min-max elementwise backward error is introduced for approximate roots of scalar polynomials $p(z)$. Compared with the elementwise relative backward error, this new measure allows for larger relative perturbations on the coeffici
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f83d50aace7d80a17a010ec7b296157a
https://lirias.kuleuven.be/handle/123456789/662541
https://lirias.kuleuven.be/handle/123456789/662541
Publikováno v:
ACM Communications in Computer Algebra. 52:78-81
In this poster we present the results of [10]. We consider the problem of finding the common roots of a set of polynomial functions defining a zero-dimensional ideal I in a ring R of polynomials over C. We propose a general algebraic framework to fin
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c178eb1baa82a9bf700a4a5c344f0984
https://doi.org/10.1145/3313880.3313888
https://doi.org/10.1145/3313880.3313888
Publikováno v:
ETNA - Electronic Transactions on Numerical Analysis. 51:451-468
A general framework for oblique projections of non-Hermitian matrices onto rational Krylov subspaces is developed. To obtain this framework we revisit the classical rational Krylov subspace algorithm and prove that the projected matrix can be written
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::10369cf8b5b5304c68c70eddfe369f4f
https://doi.org/10.1553/etna_vol51s451
https://doi.org/10.1553/etna_vol51s451
The problem of computing recurrence coefficients of sequences of rational functions orthogonal with respect to a discrete inner product is formulated as an inverse eigenvalue problem for a pencil of Hessenberg matrices. Two procedures are proposed to
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ef3ff393f2d5143192e604854f50b677
http://arxiv.org/abs/2103.04788
http://arxiv.org/abs/2103.04788