Recent Advances in Lanczos-Based Iterative Methods for Nonsymmetric Linear Systems
نویسنده
چکیده
In recent years, there has been a true revival of the nonsymmetric Lanczos method. On the one hand, the possible breakdowns in the classical algorithm are now better understood, and so-called look-ahead variants of the Lanczos process have been developed, which remedy this problem. On the other hand, various new Lanczos-based iterative schemes for solving nonsymmetric linear systems have been proposed. This paper gives a survey of some of these recent developments.
منابع مشابه
On Squaring Krylov Subspace Iterative Methods for Nonsymmetric Linear Systems
The Biorthogonal Lanczos and the Biconjugate Gradients methods have been proposed as iterative methods to approximate the solution of nonsymmetric and indefinite linear systems. Sonneveld [19] obtained the Conjugate Gradient Squared by squaring the matrix polynomials of the Biconjugate Gra dients method. Here we square the Biorthogonal Lanczos, the Biconjugate Residual and the Biconjugate Orth...
متن کاملThe BiCOR and CORS Iterative Algorithms for Solving Nonsymmetric Linear Systems
We present two iterative algorithms for solving real nonsymmetric and complex nonHermitian linear systems of equations and that were developed from variants of the nonsymmetric Lanczos method. In this paper, we give the theoretical background of the two iterative methods and discuss their main computational aspects. Using a large number of numerical experiments, we analyze their convergence pro...
متن کاملOn the squared unsymmetric Lanczos method
The biorthogonal Lanczos and the biconjugate gradient methods have been proposed as iterative methods to approximate the solution of nonsymmetric and indefinite linear systems. Sonneveld (1989) obtained the conjugate gradient squared by squaring the matrix polynomials of the biconjugate gradient method. Here we square the unsymmetric (or biorthogonal) Lanczos method for computing the eigenvalue...
متن کاملNew variants of the global Krylov type methods for linear systems with multiple right-hand sides arising in elliptic PDEs
In this paper, we present new variants of global bi-conjugate gradient (Gl-BiCG) and global bi-conjugate residual (Gl-BiCR) methods for solving nonsymmetric linear systems with multiple right-hand sides. These methods are based on global oblique projections of the initial residual onto a matrix Krylov subspace. It is shown that these new algorithms converge faster and more smoothly than the Gl-...
متن کاملModel reduction via an LFT-based explicitly restarted nonsymmetric Lanczos algorithm
The nonsymmetric Lanczos algorithm, which belongs to the class of Krylov subspace methods, is increasingly being used for model reduction of large scale systems of the form f(s) = c (sI−A)−1b, to exploit the sparse structure and reduce the computational burden. However, a good approximation is, usually, achieved only with relatively high order reduced models. Moreover, the computational cost of...
متن کامل