A TWO-LEVEL ITERATIVE SCHEME FOR GENERAL SPARSE LINEAR SYSTEMS BASED ON APPROXIMATE SKEW-SYMMETRIZERS

MANGUOĞLU M., Mehrmann V.

ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS, cilt.54, ss.370-391, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 54
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1553/etna_vol54s370
  • Dergi Adı: ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.370-391
  • Anahtar Kelimeler: Key words, symmetrizer, skew-symmetrizer, Krylov subspace method, shifted skew-symmetric system, skew-Lanczos method, MINIMAL RESIDUAL ALGORITHM, INDEFINITE
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

We propose a two-level iterative scheme for solving general sparse linear systems. The proposed scheme consists of a sparse preconditioner that increases the norm of the skew-symmetric part relative to the rest and makes the main diagonal of the coefficient matrix as close to the identity as possible so that the preconditioned system is as close to a shifted skew-symmetric matrix as possible. The preconditioned system is then solved via a particular Minimal Residual Method for Shifted Skew-Symmetric Systems (MRS). This leads to a two-level (inner and outer) iterative scheme where the MRS has short-term recurrences and satisfies an optimality condition. A preconditioner for the inner system is designed via a skew-symmetry-preserving deflation strategy based on the skew-Lanczos process. We demonstrate the robustness of the proposed scheme on sparse matrices from various applications.