Computing eigenspaces with specified eigenvalues of a regular matrix pair \((A,B)\) and condition estimation: Theory, algorithms and software
A regular matrix pair \((A,B)\) and \((A-\lambda B)\) matrix pencils are considered. A pair of deflating subspaces with specified eigenvalues, error bounds of the eigenvalues and eigenspaces, condition estimation are computed using LAPACK software. The direct orthogonal transformation method for reordering eigenvalues in the generalized Schur form is overviewed. Direct reordering algorithms with generalized backward stability are discussed. The solution of a generalized Sylvester equation is involved. Theory and algorithms for computing condition numbers and error bounds for eigenvalues and deflating subspaces of a regular matrix are collected. A FORTRAN 77 software for computing deflating subspaces with specified eigenvalues, condition numbers and error bounds is developed and described. Computational experiments that illustrate the accuracy and reliability of the software are carried out.
scientific article; zbMATH DE number 946977
scientific article