Refined and refined harmonic Jacobi--Davidson methods for computing several GSVD components of a large regular matrix pair
For researchers needing efficient computation of GSVD components from large matrix pairs, this work provides improved algorithms that address convergence issues of prior methods.
The authors propose three refined Jacobi-Davidson type methods (RCPF-JDGSVD, RCPF-HJDGSVD, RIF-HJDGSVD) for computing several GSVD components of large regular matrix pairs, which overcome erratic behavior and possible non-convergence of previous methods. Numerical experiments show RCPF-JDGSVD is better for extreme components, while the other two suit interior components.
Three refined and refined harmonic extraction-based Jacobi--Davidson (JD) type methods are proposed, and their thick-restart algorithms with deflation and purgation are developed to compute several generalized singular value decomposition (GSVD) components of a large regular matrix pair. The new methods are called refined cross product-free (RCPF), refined cross product-free harmonic (RCPF-harmonic) and refined inverse-free harmonic (RIF-harmonic) JDGSVD algorithms, abbreviated as RCPF-JDGSVD, RCPF-HJDGSVD and RIF-HJDGSVD, respectively. The new JDGSVD methods are more efficient than the corresponding standard and harmonic extraction-based JDSVD methods proposed previously by the authors, and can overcome the erratic behavior and intrinsic possible non-convergence of the latter ones. Numerical experiments illustrate that RCPF-JDGSVD performs better for the computation of extreme GSVD components while RCPF-HJDGSVD and RIF-HJDGSVD suit better for that of interior GSVD components.