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In this paper, we study shifted restated full orthogonalization method with deflation for simultaneously solving a number of shifted systems of linear equations. Theoretical analysis shows that with the deflation technique, the new residual of shifted restarted FOM is still collinear with each other. Hence, the new approach can solve the shifted systems simultaneously based on the same Krylov subspace. Numerical experiments show that the deflation technique can significantly improve the convergence performance of shifted restarted FOM.

The Conjugate Orthogonal Conjugate Residual (COCR) method [T. Sogabe and S.-L. Zhang, JCAM, 199 (2007), pp. 297-303.] has recently been proposed for solving complex symmetric linear systems. In the present paper, we develop a variant of the COCR method that allows the efficient solution of complex symmetric shifted linear systems. Some numerical examples arising from large-scale electronic structure calculations are presented to illustrate the performance of the variant.

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Restarted Full Orthogonalization Method with Deflation for Shifted Linear Systems

An Extension of the COCR Method to Solving Shifted Linear Systems with Complex Symmetric Matrices

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2 results

Restarted Full Orthogonalization Method with Deflation for Shifted Linear Systems

An Extension of the COCR Method to Solving Shifted Linear Systems with Complex Symmetric Matrices