Further improvements in nonsymmetric hybrid
نویسندگان
چکیده
In the past few years new methods have been proposed that can be seen as combinations of standard Krylov subspave methods, such as Bi{ CG and GMRES. One of the rst hybrid schemes of this type is CGS, actually the Bi{CG squared method. Other such hybrid schemes include BiCGSTAB (a combination of Bi{CG and GMRES(1)), QMRS, TFQMR, Hybrid GMRES (polynomial preconditioned GMRES) and the nested GMRESR method (GMRES preconditioned by itself or other schemes). These methods have been successful in solving relevant sparse nonsymmetric linear systems, but there is still a need for further improvements. In this paper we will highlight some of the recent advancements in the search for eeective iterative solvers.
منابع مشابه
A hybrid block GMRES method for nonsymmetric systems with multiple right-hand sides
The block GMRES (BGMRES) method is a natural generalization of the GMRES algorithm for solving large nonsymmetric systems with multiple right-hand sides. Unfortunately, its cost increases significantly per iteration, frequently rendering the method impractical. In this paper we propose a hybrid block GMRES method which offers significant performance improvements over BGMRES. This method uses th...
متن کاملCR 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...
متن کاملOn Aggressive Early Deflation in Parallel Variants of the QR Algorithm
The QR algorithm computes the Schur form of a matrix and is by far the most popular approach for solving dense nonsymmetric eigenvalue problems. Multishift and aggressive early deflation (AED) techniques have led to significantly more efficient sequential implementations of the QR algorithm during the last decade. More recently, these techniques have been incorporated in a novel parallel QR alg...
متن کاملFurther Improvements in Nonsymmetric Hybrid Iterative Methods
In the past few years new methods have been proposed that can be seen as combinations of standard Krylov subspace methods, such as Bi-CG and GMRES. Such hybrid schemes include CGS, BiCGSTAB, QMRS, TFQMR, and the nested GMRESR method. These methods have been successful in solving relevant sparse nonsymmetric linear systems, but there is still a need for further improvements. In this paper we wil...
متن کاملFurther Pieri-type formulas for the nonsymmetric Macdonald polynomial
The branching coefficients in the expansion of the elementary symmetric function multiplied by a symmetric Macdonald polynomial Pκ(z) are known explicitly. These formulas generalise the known r = 1 case of the Pieri-type formulas for the nonsymmetric Macdonald polynomials Eη(z). In this paper, we extend beyond the case r = 1 for the nonsymmetric Macdonald polynomials, giving the full generalisa...
متن کامل