Nested Krylov Methods for Shifted Linear Systems

Nested Krylov Methods for Shifted Linear Systems

and {ωk}k=1 ∈ C is a sequence of n distinct shifts. For example, shifted linear systems arise in model order reduction as well as in the geophysical exploration of both acoustic and elastic waves. In our application, we focus on wave propagation through elastic media in a frequency-domain formulation. This formulation has specific advantages when modeling visco-elastic effects. In order to impr...

DELFT UNIVERSITY OF TECHNOLOGY REPORT 14-01 Nested Krylov methods for shifted linear systems

No part of the Journal may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission from Summary Shifted linear systems are of the form (A − σ k I)x k = b, (1) where A ∈ C N ×N , b ∈ C N and {σ k } Nσ k=1 ∈ C is a sequence of numbers, called shifts. In order to so...

Krylov space solvers for shifted linear systems

We investigate the application of Krylov space methods to the solution of shifted linear systems of the form (A+ σ)x− b = 0 for several values of σ simultaneously, using only as many matrix-vector operations as the solution of a single system requires. We find a suitable description of the problem, allowing us to understand known algorithms in a common framework and developing shifted methods b...

Krylov Subspace Recycling for Sequences of Shifted Linear Systems

We study the use of Krylov subspace recycling for the solution of a sequence of slowlychanging families of linear systems, where each family consists of shifted linear systems that differ in the coefficient matrix only by multiples of the identity. Our aim is to explore the simultaneous solution of each family of shifted systems within the framework of subspace recycling, using one augmented su...

Krylov subspace methods for solving linear systems