Diagonalization of complex symmetric matrices: Generalized Householder reflections, iterative deflation and implicit shifts

摘要

AbstractWe describe a matrix diagonalization algorithm for complex symmetric (not Hermitian) matrices,A?=A?T, which is based on a two-step algorithm involving generalized Householder reflections based on the indefinite inner product?u?,v???=∑iuivi. This inner product is linear in both arguments and avoids complex conjugation. The complex symmetric input matrix is transformed to tridiagonal form using generali