A Block QMR Method for Computing Multiple Simultaneous Solutions to Complex Symmetric Systems

Boyse, W.E.; Seidl, A

doi:10.1137/0917019

Cited by 33 publications

(41 citation statements)

References 9 publications

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“…This fact was fully exploited by Freund in [124], where a QMR procedure (quasi-minimum residual norm in the Euclidean inner product) applied to this simplified Lanczos recurrence is proposed and tested. In practice, the redundant auxiliary recurrence is not constructed, and the indefinite inner product (13.1) is used throughout; we refer to Boyse and Seidl [40], and [294], as well as the references therein for a more complete discussion on using (13.1) with complex symmetric matrices.…”

Section: Complex Symmetric Matricesmentioning

confidence: 99%

Recent computational developments in Krylov subspace methods for linear systems

Simoncini

Szyld

2006

Numerical Linear Algebra App

312

254

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Abstract. Many advances in the development of Krylov subspace methods for the iterative solution of linear systems during the last decade and a half are reviewed. These new developments include different versions of restarted, augmented, deflated, flexible, nested, and inexact methods. Also reviewed are methods specifically tailored to systems with special properties such as special forms of symmetry and those depending on one or more parameters.

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Section: Complex Symmetric Matricesmentioning

confidence: 99%

Recent computational developments in Krylov subspace methods for linear systems

Simoncini

Szyld

2006

Numerical Linear Algebra App

312

254

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“…The basis vectors in this block method are constructed in a vector-wise approach. Another variant of BQMR for complex symmetric systems is the one of Boyse & Seidl (1996); the differences between these two approaches are discussed in . The structure of the BQMR algorithm is more complicated than of the BGMRES; for implementation details we refer the reader to 1) One mesh which includes all or a subset of the sources is used for the discretization.…”

Section: Block Solversmentioning

confidence: 99%

“…For a detailed overview on block Krylov subspace methods we refer the reader to Gutknecht (2007). During the last two decades, several different block solvers have been developed and applied to many problems, ranging from electromagnetic scattering (Boyse & Seidl 1996) to acoustic full waveform inversion (Calandra et al 2012). …”

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confidence: 99%

A review of block Krylov subspace methods for multisource electromagnetic modelling

Puzyrev¹,

María

2015

Geophys. J. Int.

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SUMMARYPractical applications of controlled-source electromagnetic modeling require solutions for multiple sources at several frequencies, thus leading to a dramatic increase of the computational cost. In this paper we present an approach using block Krylov subspace solvers that are iterative methods especially designed for problems with multiple right-hand-sides. Their main advantage is the shared subspace for approximate solutions, hence, these methods are expected to converge in less iterations than the corresponding standard solver applied to each linear system. Block solvers also share the same preconditioner, which is constructed only once. Simultaneously computed block operations have better utilization of cache due to the less frequent access to the system matrix. In this paper we implement two different block solvers for sparse matrices resulting from the finitedifference and the finite-element discretizations, discuss the computational cost of the algorithms and study their dependence on the number of right-hand sides given at once. The effectiveness of the proposed methods is demonstrated on two electromagnetic survey scenarios, including a large marine model. As the results of the simulations show, when a powerful preconditioning is employed, block methods are faster than standard iterative techniques in terms of both iterations and time.

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“…Multiple linear systems (1) arise in many problems in scientific computing and engineering application, including recursive least squares computations [1,2], wave scattering problems [3,4], numerical methods for integral equations [4,5], and image restorations [6]. …”

Section: Introductionmentioning

confidence: 99%