Short-Recurrence and -Storage Recycling of large Krylov-Subspaces for Sequences of Linear Systems with changing Right-Hand-Sides
This work addresses the computational bottleneck of solving multiple linear systems with the same matrix, offering a memory-efficient approach for numerical linear algebra applications.
The paper introduces new iterative methods for solving sequences of linear systems with a fixed matrix and changing right-hand sides, enabling efficient recycling of subspace information from previous solutions using short recurrences and minimal storage.
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.