A Survey of Numerical Methods for Shifted Linear Systems : Use of Shift-Invariance Property of Krylov Subspaces

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  • 大規模シフト線形方程式の数値解法 : クリロフ部分空間の性質に着目して
  • ダイキボ シフト センケイ ホウテイシキ ノ スウチカイホウ クリロフ ブブン クウカン ノ セイシツ ニ チャクモク シテ

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Abstract

Shifted linear systems arise in many important applications such as lattice quantum chromodynamics, large-scale electronic structure theory, and quadratic optimization problems. Recent strong need for solving the extremely large shifted linear systems enhance the importance of designing efficient solvers. As a candidate to satisfy the need, iterative methods using Krylov subspaces and the shift-invariance property have been attracting much interest. The primary aim of this paper is to survey the successful iterative methods and to classify them in terms of Krylov subspace methods.

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