Restarted weighted full orthogonalization method for shifted linear systems

Restarted weighted full orthogonalization method for shifted linear systems

It is known that the restarted full orthogonalization method (FOM) outperforms the restarted generalized minimum residual method (GMRES) in several circumstances for solving shifted linear systems when the shifts are handled simultaneously. On the basis of theWeightedArnoldi process, aweighted version of the Restarted Shifted FOM is proposed, which can provide accelerating convergence rate with...

Restarted Full Orthogonalization Method for Shifted Linear Systems

Restarted GMRES is known to be inefficient for solving shifted systems when the shifts are handled simultaneously. Variants have been proposed to enhance its performance. We show that another restarted method, restarted Full Orthogonalization Method (FOM), can effectively be employed. The total number of iterations of restarted FOM applied to all shifted systems simultaneously is the same as th...

A METHOD FOR SOLVING FUZZY LINEAR SYSTEMS

In this paper we present a method for solving fuzzy linear systemsby two crisp linear systems. Also necessary and sufficient conditions for existenceof solution are given. Some numerical examples illustrate the efficiencyof the method.

Defuzzification method for solving fuzzy linear systems

Efficient Preconditioner Updates for Shifted Linear Systems

We present a new technique for building effective and low cost preconditioners for sequences of shifted linear systems (A + αI)xα = b, where A is symmetric positive definite and α > 0. This technique updates a preconditioner for A, available in the form of an LDLT factorization, by modifying only the nonzero entries of the L factor in such a way that the resulting preconditioner mimics the diag...