Enclosing all zeros of a system of analytic functions

被引：0

作者：

Dahne, J. ^{[1
]}

Ciappina, M. F. ^{[2
,3
]}

Tucker, W. ^{[1
]}

机构：

[1] Uppsala Univ, Dept Math, Box 480, Uppsala, Sweden

[2] Max Planck Inst Quantum Opt, Hans Kopfermann Str 1, D-85748 Garching, Germany

[3] ASCR, Inst Phys, ELI Beamlines Project, Na Slovance 2, Prague 18221, Czech Republic

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2019年 / 348卷

基金：

瑞典研究理事会;

关键词：

Rigorous numerics; Argument principle; Root finding; Interval analysis; Systems of analytic functions;

D O I：

10.1016/j.amc.2018.08.041

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a rigorous numerical method for location of simple zeros of a system of two analytic functions in a rectangular cuboid domain based on the logarithmic integral. We compare this to a simpler, also rigorous, method based on bisection. The latter is determined to be more efficient in the examples considered. This is mainly due to inefficient methods for computing the logarithmic integral occurring in the former method. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：513 / 522

页数：10

共 50 条

[31] ON THE ZEROS OF A CLASS OF POLYNOMIALS AND RELATED ANALYTIC FUNCTIONS
A. Aziz
B. A. Zargar
AnalysisinTheoryandApplications, 2012, 28 (02) : 180 - 188
[32] On location and approximation of clusters of zeros of analytic functions
Giusti, M
Lecerf, G
Salvy, B
Yakoubsohn, JC
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2005, 5 (03) : 257 - 311
[33] ZEROS OF ANALYTIC FUNCTIONS AND NORMS OF INVERSE MATRICES
Gluskin, E.
Meyer, M.
Pajor, A.
ISRAEL JOURNAL OF MATHEMATICS, 1994, 87 (1-3) : 225 - 242
[34] THE ANGULAR DISTRIBUTION OF ZEROS OF RANDOM ANALYTIC FUNCTIONS
Mahola, M. P.
Filevych, P. V.
UFA MATHEMATICAL JOURNAL, 2012, 4 (01): : 115 - 127
[35] LOWER BOUNDS FOR ZEROS OF ANALYTIC-FUNCTIONS
IFANTIS, EK
KOURIS, CB
NUMERISCHE MATHEMATIK, 1977, 27 (02) : 239 - 247
[36] On the zeros of a class of polynomials and related analytic functions
Jain, VK
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 1997, 28 (04): : 533 - 549
[37] ON ZEROS OF MATRIX-VALUED ANALYTIC FUNCTIONS
Monga, Z. B.
Shah, W. M.
OPERATORS AND MATRICES, 2023, 17 (02): : 383 - 391
[38] ZEROS OF LIPSCHITZ FUNCTIONS ANALYTIC IN UNIT DISC
TAYLOR, BA
WILLIAMS, DL
MICHIGAN MATHEMATICAL JOURNAL, 1971, 18 (02) : 129 - &
[39] Counting Functions of Zeros of Analytic Functions in Spaces with Mixed Norm
Dolgoborodov, A. A.
RUSSIAN MATHEMATICS, 2012, 56 (10) : 15 - 25
[40] Counting functions of zeros of analytic functions in spaces with mixed norm
A. A. Dolgoborodov
Russian Mathematics, 2012, 56 (10) : 15 - 25

← 1 2 3 4 5 →