Flexible GPBi-CG Method for Nonsymmetric Linear Systems

Flexible GPBi-CG Method for Nonsymmetric Linear Systems

We present a flexible version of GPBi-CG algorithm which allows for the use of a different preconditioner at each step of the algorithm. In particular, a result of the flexibility of the variable preconditioner is to use any iterative method. For example, the standard GPBi-CG algorithm itself can be used as a preconditioner, as can other Krylov subspace methods or splitting methods. Numerical e...

The flexible incomplete LU preconditioner for large nonsymmetric linear systems

The ILU factorization is one of the most popular preconditioners for the Krylov subspace method, alongside the GMRES. Properties of the preconditioner derived from the ILU factorization are relayed onto the dropping rules. Recently, Zhang et al. [Numer. Linear. Algebra. Appl., Vol. 19, pp. 555–569, 2011] proposed a Flexible incomplete Cholesky (IC) factorization for symmetric linear systems. Th...

A Bi-CG type iterative method for Drazin-inverse solution of singular inconsistent nonsymmetric linear systems of arbitrary index

CR Variants of Hybrid Bi-CG Methods for Solving Linear Systems with Nonsymmetric Matrices

s at ICCAM 2008 CR Variants of Hybrid Bi-CG Methods for Solving Linear Systems with Nonsymmetric Matrices Kuniyoshi Abe Gifu Shotoku University 1-38, Nakauzura, Gifu, 500-8288 Japan [email protected] Joint work with: S. Fujino By Krylov subspace methods, we are solving a large sparse linear system Ax = b, where A stand for an n-by-n matrix, and x and b are n-vectors, respectively. The Bi-C...

A Parallel Krylov-Type Method for Nonsymmetric Linear Systems

Parallel Krylov (S-step and block) iterative methods for linear systems have been studied and implemented in the past. In this article we present a parallel Krylov method based on block s-step method for nonsymmetric linear systems. We derive two new averaging algorithm to combine several approximations to the solution of a single linear system using the block method with multiple initial guess...