Some Generalizations and Modifications of Iterative Methods for Solving Large Sparse Symmetric Indefinite Linear Systems
نویسندگان
چکیده
and Applied Analysis 3 Instead of solving for y directly from the triangular linear system (15), Paige and Saunders [1] factorize the matrix Tn into a lower triangular matrix with bandwidth three (resulting in the SYMMLQmethod). Also, we have TnQn−1 = ̂ Ln = [ [ [ [ [ [ [ [ [ [ γ0 δ1 γ1 ε2 δ2 γ2 d d d εn−3 δn−3 γn−3 εn−2 δn−2 γn−2 εn−1 δn−1 γn−1 ] ] ] ] ] ] ] ] ]
منابع مشابه
Preconditioned Generalized Minimal Residual Method for Solving Fractional Advection-Diffusion Equation
Introduction Fractional differential equations (FDEs) have attracted much attention and have been widely used in the fields of finance, physics, image processing, and biology, etc. It is not always possible to find an analytical solution for such equations. The approximate solution or numerical scheme may be a good approach, particularly, the schemes in numerical linear algebra for solving ...
متن کاملOn solving sparse symmetric linear systems whose definiteness is unknown
Solving a large, sparse, symmetric linear system Ax = b iteratively must use appropriate methods. The conjugate gradient (CG) method can break down if A is indefinite while algorithms such as SYMMLQ and MINRES, though stable for indefinite systems, are computationally more expensive than CG when applied to positive definite matrices. In this paper, we present an iterative method for the case wh...
متن کاملPreconditioned Iterative Methods for Homotopy Curve Tracking
Homotopy algorithms are a class of methods for solving systems of nonlinear equations that are globally convergent with probability one. All homotopy algorithms are based on the construction of an appropriate homotopy map and then the tracking of a curve in the zero set of this homotopy map. The fundamental linear algebra step in these algorithms is the computation of the kernel of the homotopy...
متن کاملComparison of some Preconditioned Krylov Methods for Solving Sparse Non-symmetric Linear Systems of Equations
Large sparse non-symmetric linear systems of equations often occur in many scientific and engineering applications. In this paper, we present a comparative study of some preconditioned Krylov iterative methods, namely CGS, Bi-CGSTAB, TFQMR and GMRES for solving such systems. To demonstrate their efficiency, we test and compare the numerical implementations of these methods on five numerical exa...
متن کاملA QR-decomposition of block tridiagonal matrices generated by the block Lanczos process
For MinRes and SymmLQ it is essential to compute a QR decomposition of a tridiagonal coefficient matrix gained in the Lanczos process. This QR decomposition is constructed by an update scheme applying in every step a single Givens rotation. Using complex Householder reflections we generalize this idea to block tridiagonal matrices that occur in generalizations of MinRes and SymmLQ to block meth...
متن کامل