Short-Recurrence and -Storage Recycling of large Krylov-Subspaces for Sequences of Linear Systems with changing Right-Hand-Sides

TL;DR

This paper introduces new iterative methods that efficiently recycle Krylov subspace information for solving sequences of linear systems with changing right-hand sides, using short recurrences and minimal storage.

Contribution

It presents novel principles and methods based on the IDR-theorem and Horner scheme to improve efficiency in solving related linear systems.

Findings

Methods reduce storage requirements

Recycling improves computational efficiency

Applicable to large Krylov subspaces

Abstract

In this text I present a couple of new principles and thereon based iterative methods for numerical solution of sequences of systems of linear equations with fixed system matrix and changing right-hand-sides. The use of the new methods is to recycle all subspace information that is obtained anyway in the solution process of a former system, to solve subsequent systems. All these principles and methods are based on short recurrences and small storage requirements. The principles are based on the IDR-theorem and the Horner scheme for polynomials.