2013/04/06 by Matthias Petschow, Petschow, Matthias, Enrique S. Quintana–Ort́ı +3 · 1 citation
Computer Science · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Software (cs.MS) #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical Methods and Algorithms #Numerical methods for differential equations #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1304.1864
openalex publication_date 2013/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The real symmetric tridiagonal eigenproblem is of outstanding importance in\nnumerical computations; it arises frequently as part of eigensolvers for\nstandard and generalized dense Hermitian eigenproblems that are based on a\nreduction to tridiagonal form. For its solution, the algorithm of Multiple\nRelatively Robust Representations (MRRR) is among the fastest methods. Although\nfast, the solvers based on MRRR do not deliver the same accuracy as competing\nmethods like Divide & Conquer or the QR algorithm. In this paper, we\ndemonstrate that the use of mixed precisions leads to improved accuracy of\nMRRR-based eigensolvers with limited or no performance penalty. As a result, we\nobtain eigensolvers that are not only equally or more accurate than the best\navailable methods, but also -in most circumstances- faster and more scalable\nthan the competition.\n