In this paper, we propose different algorithms for the solution of a tensor linear discrete ill-posed problem arising in application meshless method solving PDEs three-dimensional space using multiquadric radial basis functions. It is well known that truncated singular value decomposition (TSVD) most common effective solver ill-conditioned systems, but unfortunately operation count system with ...

The purpose of this work is to compare the performance of some preconditioned iterative methods for solving the linear systems of equations, formed at each time-integration step of two-dimensional incompressible NavierStokes equations of fluid flow. The Navier-Stokes equations are discretized in an implicit and upwind control volume formulation. The iterative methods used in this paper include ...

Krylov subspace methods have been applied successfully to solve various problems in Numerical Linear Algebra. The Netherlands have been a pioneer country in the development of Krylov methods over the past years. Methods like the Conjugate Gradient Squared (CGS), Bi-Conjugate Gradient Stabilized (BiCGSTAB), Nested GMRES (GMRESR), and the Induced Dimension Reduction method (IDR) are examples of K...

Abstract The Krylov subspace method has been investigated and refined for approximating the behaviors of finite or infinite dimensional linear operators. It used eigenvalues, solutions equations, operator functions acting on vectors. Recently, time-series data analysis, much attention is being paid to as a viable estimating multiplications vector by an unknown referred transfer operator. In thi...

It will be shown that extended Krylov subspaces –under some assumptions– can be retrieved without any explicit inversion or system solves involved. Instead we do the necessary computations of A−1v in an implicit way using the information from an enlarged standard Krylov subspace. It is well-known that both for classical and extended Krylov spaces, direct unitary similarity transformations exist...

This article is devoted to the numerical solution of large-scale quadratic eigenvalue problems. Such problems arise in a wide variety of applications, such as the dynamic analysis of structural mechanical systems, acoustic systems, fluid mechanics, and signal processing. We first introduce a generalized second-order Krylov subspace based on a pair of square matrices and two initial vectors and ...