Spectral simplex method

被引:14
|
作者
Protasov, Vladimir Yu. [1 ]
机构
[1] Moscow MV Lomonosov State Univ, Dept Math & Mech, Moscow 119992, Russia
关键词
Iterative optimization method; Nonnegative matrix; Spectral radius; Cycling; Spectrum of a graph; Leontief model; Positive linear switching system; RADIUS; STABILITY; MATRICES; SYSTEMS; SETS;
D O I
10.1007/s10107-015-0905-2
中图分类号
TP31 [计算机软件];
学科分类号
081202 ; 0835 ;
摘要
We develop an iterative optimization method for finding the maximal and minimal spectral radius of a matrix over a compact set of nonnegative matrices. We consider matrix sets with product structure, i.e., all rows are chosen independently from given compact sets (row uncertainty sets). If all the uncertainty sets are finite or polyhedral, the algorithm finds the matrix with maximal/minimal spectral radius within a few iterations. It is proved that the algorithm avoids cycling and terminates within finite time. The proofs are based on spectral properties of rank-one corrections of nonnegative matrices. The practical efficiency is demonstrated in numerical examples and statistics in dimensions up to 500. Some generalizations to non-polyhedral uncertainty sets, including Euclidean balls, are derived. Finally, we consider applications to spectral graph theory, mathematical economics, dynamical systems, and difference equations.
引用
收藏
页码:485 / 511
页数:27
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