COMPUTING MULTIVARIATE FEKETE AND LEJA POINTS BY NUMERICAL LINEAR ALGEBRA

被引：88

作者：

Bos, L. ^{[1
]}

De Marchi, S. ^{[2
]}

Sommariva, A. ^{[2
]}

Vianello, M. ^{[2
]}

机构：

[1] Univ Verona, Dept Comp Sci, I-37134 Verona, Italy

[2] Univ Padua, Dept Pure & Appl Math, I-35121 Padua, Italy

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2010年 / 48卷 / 05期

关键词：

weakly admissible meshes; approximate Fekete points; discrete Leja points; Vandermonde matrices; QR factorization with column pivoting; LU factorization with row pivoting; pluripotential theory; equilibrium measure; POLYNOMIAL INTERPOLATION; APPROXIMATION;

D O I：

10.1137/090779024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We discuss and compare two greedy algorithms that compute discrete versions of Fekete-like points for multivariate compact sets by basic tools of numerical linear algebra. The first gives the so-called approximate Fekete points by QR factorization with column pivoting of Vandermonde-like matrices. The second computes discrete Leja points by LU factorization with row pivoting. Moreover, we study the asymptotic distribution of such points when they are extracted from weakly admissible meshes.

引用

页码：1984 / 1999

页数：16

共 34 条

[1]

[Anonymous], 1991, LONDON MATH SOC MONO

[2]

[Anonymous], 1997, Logarithmic Potentials with External Fields

[3]

BAGLAMA J., 1998, ELECTRON T NUMER ANA, V7, P124

[4] Estimation of Fekete points [J].

Bendito, E. ;

Carmona, A. ;

Encinas, A. M. ;

Gesto, J. M. .

JOURNAL OF COMPUTATIONAL PHYSICS, 2007, 225 (02) :2354-2376

[5]

Berman R., ACTA MATH IN PRESS

[6]

BIALASCIEZ L, ANN MAT P 4 IN PRESS

[7] POLYNOMIAL INTERPOLATION OF HOLOMORPHIC-FUNCTIONS IN C AND CN [J].

BLOOM, T ;

BOS, L ;

CHRISTENSEN, C ;

LEVENBERG, N .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1992, 22 (02) :441-470

[8]

Bos L, 2001, MATH COMPUT, V70, P1543, DOI 10.1090/S0025-5718-00-01262-X

[9]

BOS L, MATH COMP IN PRESS

[10]

Bos LP, 2008, ELECTRON T NUMER ANA, V30, P377

← 1 2 3 4 →