Zobrazeno 1 - 10
of 11
pro vyhledávání: '"Leili Rafiee Sevyeri"'
Publikováno v:
SIAM Review. 62:231-243
We look at two classical examples in the theory of numerical analysis, namely the Runge example for interpolation and Wilkinson's example (actually two examples) for rootfinding. We use the modern theory of backward error analysis and conditioning, a
Publikováno v:
ACM Communications in Computer Algebra. 53:103-106
In general, finding the Greatest Common Divisor (GCD) of two exactly-known univariate polynomials is a well understood problem. However, it is also known that the GCD problem for noisy polynomials (polynomials with errors in their coefficients) is il
Publikováno v:
Journal of Approximation Theory. 283:105810
Publikováno v:
Experimental Mathematics. 31:184-191
We give an apparently new proof of Stirling’s original asymptotic formula for the behavior of ln z! for large z. Stirling’s original formula is not the formula widely known as “Stirling’s formula”,...
Publikováno v:
ISSAC
One useful standard method to compute eigenvalues of matrix polynomials ${\bf P}(z) \in \mathbb{C}^{n\times n}[z]$ of degree at most $\ell$ in $z$ (denoted of grade $\ell$, for short) is to first transform ${\bf P}(z)$ to an equivalent linear matrix
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::54ebd5f29c2bf9aba03ea916e2e794c8
http://arxiv.org/abs/2102.09726
http://arxiv.org/abs/2102.09726
Publikováno v:
SYNASC
For a pair of polynomials with real or complex coefficients, given in any particular basis, the problem of finding their GCD is known to be ill-posed. An answer is still desired for many applications, however. Hence, looking for a GCD of so-called ap
Publikováno v:
Computer Algebra in Scientific Computing ISBN: 9783030600259
CASC
CASC
Parametric linear systems are linear systems of equations in which some symbolic parameters, that is, symbols that are not considered to be candidates for elimination or solution in the course of analyzing the problem, appear in the coefficients of t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c45573ddc41b2ff0f33f6a39b49f7752
https://doi.org/10.1007/978-3-030-60026-6_11
https://doi.org/10.1007/978-3-030-60026-6_11
Publikováno v:
Communications in Computer and Information Science ISBN: 9783030412579
MC
MC
We adapt Victor Y. Pan’s root-based algorithm for finding approximate GCD to the case where the polynomials are expressed in Bernstein bases. We use the numerically stable companion pencil of Guðbjorn Jonsson to compute the roots, and the Hopcroft
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::849cc94541d42b529d81989c51970134
https://doi.org/10.1007/978-3-030-41258-6_6
https://doi.org/10.1007/978-3-030-41258-6_6
We define \emph{generalized standard triples} $\mathbf{X}$, $\mathbf{Y}$, and $L(z) = z\mathbf{C}_{1} - \mathbf{C}_{0}$, where $L(z)$ is a linearization of a regular matrix polynomial $\mathbf{P}(z) \in \mathbb{C}^{n \times n}[z]$, in order to use th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ed4995b301905aa1623fe346dc4f0072
http://arxiv.org/abs/1805.04488
http://arxiv.org/abs/1805.04488
Publikováno v:
ACM Communications in Computer Algebra. 51:21-22
We want to investigate on the sequence of minimal polynomials of the sequence below.