Two complementary block Macaulay matrix algorithms to solve multiparameter eigenvalue problems
The paper deals with Multiparameter Eigenvalue Problems (MEPs) which here are solved by two algorithms using the block Macaulay matrix. The first algorithm exploits the structure of the null space of the block Macaulay matrix in order to find the solution of the considered MEP, according to an approach already presented by the authors. On the other hand, the second algorithm considers the column space of the block Macaulay matrix. The intrinsic complementarity between both fundamental subspaces allows one to build a new complementary algorithm to solve MEPs. This column space based algorithm does not require an explicit computation of a numerical basis matrix of the null space, but considers the data in the columns of the block Macaulay matrix directly and removes the influence of the solutions at infinity implicitly via a backward QR-decomposition. Several significant numerical examples are reported to clarify the use of both algorithms.
scientific article; zbMATH DE number 7597861
scientific article