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Article information
1998 , Volume 3, ¹ 2, p.21-30
Lakeyev A.V.
An exact upper estimate of the spectral radius of nonexpanding matrices
In this paper, it is shown that a real Cayley transformation
establishes one-to-one correspondence between P-matrices and
nonexpanding matrices that play one of the leads in the computation of algebraic solutions to interval linear equations. Relying on the correspondence constructed, we prove that the problem of checking whether a matrix is nonexpanding or not is co-NP-complete, and obtain
unimprovable upper estimations for the spectral radius, determinant and sum of principal minors of nonexpanding matrices.
[full text] Classificator Msc2000:- *65F15 Eigenvalues, eigenvectors
- 65F30 Other matrix algorithms
- 65F40 Determinants
- 65G30 Interval and finite arithmetic
Classificator Computer Science:- *G.1.0 General (Numerical Analysis)
- G.1.3 Numerical Linear Algebra
Keywords: nonexpanding matrx,co-NP-complete problem, interval matrix, nonsingularity radius, interval analysis, nonexpanding matrix, positive matrix, NP-completeness, Cayley transformation, spectral radius, determinant, sums of principal minors
Author(s):
Lakeyev Anatoly Valentinovich
Dr.
Position: Leading research officer
Office: Matrosov Institute for System Dynamics and Control Theory of the Siberian Branch of Russian Academy of Sciences
Address: 664033, Russia, Irkutsk, Lermontov str., 134
E-mail: lakeyev@icc.ru
SPIN-code: 3525-6659
Bibliography link:
Lakeyev A.V. An exact upper estimate of the spectral radius of nonexpanding matrices // Computational technologies. 1998. V. 3. ¹ 2. P. 21-30
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