2017/09/01 by Rafael Rodríguez‐Sánchez, Rodríguez-Sánchez, Rafael, Sandra Catalán +8
Computer Science · Engineering · #Distributed #FOS: Computer and information sciences #Mathematical Software (cs.MS) #Matrix Theory and Algorithms #Parallel #Railway Engineering and Dynamics #Structural Health Monitoring Techniques #and Cluster Computing (cs.DC)
paper · pdf · doi:10.48550/arxiv.1709.00302
openalex publication_date 2017/09/01 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We address the reduction to compact band forms, via unitary similarity\ntransformations, for the solution of symmetric eigenvalue problems and the\ncomputation of the singular value decomposition (SVD). Concretely, in the first\ncase we revisit the reduction to symmetric band form while, for the second\ncase, we propose a similar alternative, which transforms the original matrix to\n(unsymmetric) band form, replacing the conventional reduction method that\nproduces a triangular--band output. In both cases, we describe algorithmic\nvariants of the standard Level-3 BLAS-based procedures, enhanced with\nlook-ahead, to overcome the performance bottleneck imposed by the panel\nfactorization. Furthermore, our solutions employ an algorithmic block size that\ndiffers from the target bandwidth, illustrating the important performance\nbenefits of this decision. Finally, we show that our alternative compact band\nform for the SVD is key to introduce an effective look-ahead strategy into the\ncorresponding reduction procedure.\n