Interval analysis: theory and applications

被引：367

作者：

Alefeld, G

Mayer, G

机构：

[1] Univ Karlsruhe, Inst Angew Math, D-76128 Karlsruhe, Germany

[2] Univ Rostock, Fachbereich Math, D-18051 Rostock, Germany

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2000年 / 121卷 / 1-2期

关键词：

D O I：

10.1016/S0377-0427(00)00342-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give an overview on applications of interval arithmetic. Among others we discuss verification methods for linear systems of equations, nonlinear systems, the algebraic eigenvalue problem, initial value problems for ODEs and boundary value problems for elliptic PDEs of second order. We also consider the item software in this field and give some historical remarks. (C) 2000 Elsevier Science B.V. All rights reserved.

引用

页码：421 / 464

页数：44

共 118 条

[1] Adams E., 1993, SCI COMPUTING AUTOMA
[2] ALBRECHT R, 1993, VALIDATION NUMERICS
[3] CALCULABLE ERROR-BOUNDS FOR AN EIGENPAIR, INCLUDING ROUNDING ERRORS, USING THE SO-CALLED PRECISE-SCALAR-PRODUCT
ALEFELD, G
[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 1987, 67 (03): : 145 - 152
[4] Alefeld G, 1999, MATH NACHR, V208, P5
[5] THE CHOLESKY METHOD FOR INTERVAL DATA
ALEFELD, G
MAYER, G
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1993, 194 : 161 - 182
[6] NUMERICAL VALIDATION FOR AN INVERSE MATRIX EIGENVALUE PROBLEM
ALEFELD, G
GIENGER, A
MAYER, G
[J]. COMPUTING, 1994, 53 (3-4) : 311 - 322
[7] ON THE SYMMETRICAL AND UNSYMMETRIC SOLUTION SET OF INTERVAL SYSTEMS
ALEFELD, G
MAYER, G
[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1995, 16 (04) : 1223 - 1240
[8] On the shape of the symmetric, persymmetric, and skew-symmetric solution set
Alefeld, G
Kreinovich, V
Mayer, G
[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1997, 18 (03) : 693 - 705
[9] The shape of the solution set for systems of interval linear equations with dependent coefficients
Alefeld, G
Kreinovich, V
Mayer, G
[J]. MATHEMATISCHE NACHRICHTEN, 1998, 192 : 23 - 36
[10] BOUNDING THE SLOPE OF POLYNOMIAL OPERATORS AND SOME APPLICATIONS
ALEFELD, G
[J]. COMPUTING, 1981, 26 (03) : 227 - 237

← 1 2 3 4 5 6 7 8 9 10 →