Improving data re-use in eigenvalue-related computations
Gregory Mark Henry · 1994
New methods for achieving greater data reuse in serial and distributed dense linear algebra are given and applied in various eigenvalue contexts. One method is a new lookahead approach for the symmetric and unsymmetric Schur decomposition. This same lookahead approach is used to develop a block inverse iteration and shifted Hessenberg solver that is faster than older methods. Block orthogonal kernels are studied and a new strategy for Hessenberg reduction is given. The problems of multivariable frequency response and unsymmetric inverse iteration are considered as important applications of the new methodology. Models are used to design effective kernels for conventional memory hierarchies. The enhanced performance of all methods is verified through experiment.