Resumen de Regularizing algorithm for mixed matrix pencils

Tetiana Klymchuk

• P. Van Dooren 1979 constructed an algorithm for computing all singular summands of Kronecker's canonical form of a matrix pencil. His algorithm uses only unitary transformations, which improves its numerical stability. We extend Van Dooren's algorithm to square complex matrices up to consimilarity transformations A↦SA¯S−1 and to pairs of m×n complex matrices up to transformations (A,B)↦(SAR,SB¯R), in which S and R are nonsingular matrices.