An algorithm for computing the distance to instability

被引：27
作者：
He, C
Watson, GA
机构：
[1] Univ Kansas, Dept Math, Lawrence, KS 66045 USA
[2] Univ Dundee, Dept Math, Dundee DD1 4HN, Scotland
来源：
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 1998年 / 20卷 / 01期
关键词：
stable matrices; distance to instability; inverse iteration; global minimum searching;
D O I：
10.1137/S0895479897314838
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
An algorithm is developed for computing the distance to instability of an n x n matrix. It is aimed primarily at sparse matrices and can be used for any value of n provided that an eigenvalue problem for a (2n) x (2n) Hamiltonian matrix can be solved on the computer being used. The algorithm gives both a x lower bound and an upper bound for the distance in guaranteed accuracy. The method is faster than other currently available methods.
引用
收藏
页码：101 / 116
页数：16
相关论文
共 19 条
[1]  
BAI Z, 1995, TEST MATRIX COLLECTI
[2]   A REGULARITY RESULT FOR THE SINGULAR-VALUES OF A TRANSFER-MATRIX AND A QUADRATICALLY CONVERGENT ALGORITHM FOR COMPUTING ITS L-INFINITY-NORM [J].
BOYD, S ;
BALAKRISHNAN, V .
SYSTEMS & CONTROL LETTERS, 1990, 15 (01) :1-7
[3]   A FAST ALGORITHM TO COMPUTE THE H-INFINITY-NORM OF A TRANSFER-FUNCTION MATRIX [J].
BRUINSMA, NA ;
STEINBUCH, M .
SYSTEMS & CONTROL LETTERS, 1990, 14 (04) :287-293
[4]   A BISECTION METHOD FOR MEASURING THE DISTANCE OF A STABLE MATRIX TO THE UNSTABLE MATRICES [J].
BYERS, R .
SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1988, 9 (05) :875-881
[5]   ON CONDITION NUMBERS AND THE DISTANCE TO THE NEAREST ILL-POSED PROBLEM [J].
DEMMEL, JW .
NUMERISCHE MATHEMATIK, 1987, 51 (03) :251-289
[6]  
GODETHOBIE S, 1993, THESIS PARIS 9 DAUPH
[7]  
Golub G.H., 1996, Matrix Computations, Vthird
[8]   On the distance to uncontrollability and the distance to instability and their relation to some condition numbers in control [J].
He, C .
NUMERISCHE MATHEMATIK, 1997, 76 (04) :463-477
[9]   An algorithm for computing the numerical radius [J].
He, CY ;
Watson, GA .
IMA JOURNAL OF NUMERICAL ANALYSIS, 1997, 17 (03) :329-342
[10]   STABILITY RADII OF LINEAR-SYSTEMS [J].
HINRICHSEN, D ;
PRITCHARD, AJ .
SYSTEMS & CONTROL LETTERS, 1986, 7 (01) :1-10
12