A method for computing all values lambda such that A plus lambda B has a multiple eigenvalue

作者：Muhic Andrej^*; Plestenjak Bor

来源：Linear Algebra and Its Applications, 2014, 440: 345-359.

DOI：10.1016/j.laa.2013.10.015

• Singular two-parameter eigenvalue problem
• Staircase algorithm
• Double eigenvalue
• Kronecker canonical form

Given a pair of n x n matrices A and B, we consider the problem of finding values lambda such that the matrix A + lambda B has a multiple eigenvalue. Our approach solves the problem using only the standard matrix computation tools. By formulating the problem as a singular two-parameter eigenvalue problem, we construct matrices Delta(1) and Delta(0) of size 3n(2) x 3n(2) with the property that the finite regular eigenvalues of the singular pencil Delta(1) - lambda Delta(0) are the values lambda such that A + lambda B has a multiple eigenvalue. We show that these values can be computed numerically from Delta(1) and Delta(0) by the staircase algorithm.

• 出版日期2014-1-1