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of 57
pro vyhledávání: '"Stanley C. Eisenstat"'
Publikováno v:
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics, 2017, 38 (4), pp.1100-1115. ⟨10.1137/140986566⟩
SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics, 2017, 38 (4), pp.1100-1115. ⟨10.1137/140986566⟩
International audience; We derive an upper bound on the symmetric componentwise relative backward error for symmetric linear systems of equations. Since the bound can be computed efficiently and, except for some artificial examples, seems to be of th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::eabe0c492ba2bce4ee10b7315a4ea4ba
https://oatao.univ-toulouse.fr/22605/
https://oatao.univ-toulouse.fr/22605/
Autor:
Stanley C. Eisenstat, Joseph W. H. Liu
Publikováno v:
SIAM Journal on Matrix Analysis and Applications. 29:1363-1381
The elimination tree of a symmetric matrix plays an important role in sparse elimination. We recently defined a generalization of this structure to the unsymmetric case that retains many of its properties. Here we present an algorithm for constructin
Autor:
Joseph W. H. Liu, Stanley C. Eisenstat
Publikováno v:
SIAM Journal on Matrix Analysis and Applications. 26:686-705
The elimination tree of a symmetric matrix plays an important role in sparse matrix factorization. By using paths instead of edges to define the tree, we generalize this structure to unsymmetric matrices while retaining many of its properties. If we
Publikováno v:
SIAM Journal on Matrix Analysis and Applications. 20:720-755
We investigate several ways to improve the performance of sparse LU factorization with partial pivoting, as used to solve unsymmetric linear systems. We introduce the notion of unsymmetric supernodes to perform most of the numerical computation in de
Autor:
Ilse C. F. Ipsen, Stanley C. Eisenstat
Publikováno v:
BIT Numerical Mathematics. 38:502-509
Let\(\hat \lambda \) and\(\hat x\) be a perturbed eigenpair of a diagonalisable matrixA. The problem is to bound the error in\(\hat \lambda \) and\(\hat \lambda \). We present one absolute perturbation bound and two relative perturbation bounds.
Autor:
Stanley C. Eisenstat, Edward Rothberg
Publikováno v:
SIAM Journal on Matrix Analysis and Applications. 19:682-695
The minimum degree and minimum local fill algorithms are two bottom-up heuristics for reordering a sparse matrix prior to factorization. Minimum degree chooses a node of least degree to eliminate next; minimum local fill chooses a n ode whose elimina
Autor:
Ilse C. F. Ipsen, Stanley C. Eisenstat
Publikováno v:
SIAM Journal on Matrix Analysis and Applications. 20:149-158
We show that three well-known perturbation bounds for matrix eigenvalues imply relative bounds: the Bauer--Fike and Hoffman--Wielandt theorems for diagonalizable matrices, and Weyl's theorem for Hermitian matrices. As a consequence, relative perturba
Autor:
Stanley C. Eisenstat
Publikováno v:
Linear Algebra and its Applications. 416(2-3):742-744
Let A be a singular, diagonalizable matrix with group inverse A # , and let A + E be a perturbation of A . We show that each eigenvalue μ of A + E is an O(∥ A # E ∥ 2 ) relative perturbation of a nonzero eigenvalue of A , unless it is small enou
Autor:
Stanley C. Eisenstat, Homer F. Walker
Publikováno v:
SIAM Journal on Scientific Computing. 17:16-32
An inexact Newton method is a generalization of Newton’s method for solving $F(x) = 0,F:\mathbb{R}^n \to \mathbb{R}^n $in which, at the kth iteration, the step $s_k $ from the current approximate solution $x_k $ is required to satisfy a condition $
Autor:
Ilse C. F. Ipsen, Stanley C. Eisenstat
Publikováno v:
SIAM Journal on Numerical Analysis. 32:1972-1988
A technique is presented for deriving bounds on the relative change in the singular values of a real matrix (or the eigenvalues of a real symmetric matrix) due to a perturbation, as well as bounds on the angles between the unperturbed and perturbed s