Two Algorithms for Symmetric Linear Systems with Multiple Right-hand Sides
نویسنده
چکیده
In this paper, we investigate the block Lanczos algorithm for solving large sparse symmetric linear systems with multiple right-hand sides, and show how to incorporate deeation to drop converged linear systems using a natural convergence criterion, and present an adaptive block Lanczos algorithm. We propose also a block version of Paige and Saun-ders' MINRES method for iterative solution of symmetric linear systems, and describe important implementation details. We establish a relationship between the block Lanc-zos algorithm and block MINRES algorithm, and compare the numerical performance of the Lanczos algorithm and MINRES method for symmetric linear systems applied to a sequence of right-hand sides with that of the block Lanczos algorithm and block MINRES algorithm for multiple linear systems simultaneously.
منابع مشابه
New 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 کاملCG-type algorithms to solve symmetric matrix equations
The global FOM and GMRES are among the effective algorithms to solve linear system of equations with multiple right-hand sides. In this paper, we study these algorithms in the case that the coefficient matrix is symmetric and extract two CGtype algorithms for solving symmetric linear systems of equations with multiple right– hand sides. Then, we compare the numerical performance of the new algo...
متن کاملDeflated and Restarted Symmetric Lanczos Methods for Eigenvalues and Linear Equations with Multiple Right-Hand Sides
A deflated restarted Lanczos algorithm is given for both solving symmetric linear equations and computing eigenvalues and eigenvectors. The restarting limits the storage so that finding eigenvectors is practical. Meanwhile, the deflating from the presence of the eigenvectors allows the linear equations to generally have good convergence in spite of the restarting. Some reorthogonalization is ne...
متن کاملImproved seed methods for symmetric positive definite linear equations with multiple right-hand sides
We consider symmetric positive definite systems of linear equations with multiple right-hand sides. The seed conjugate gradient method solves one right-hand side with the conjugate gradient method and simultaneously projects over the Krylov subspace thus developed for the other right-hand sides. Then the next system is solved and used to seed the remaining ones. Rounding error in the conjugate ...
متن کاملBlock Algorithms for Quark Propagator Calculation
Computing quark propagators in lattice QCD is equivalent to solving large, sparse linear systems with multiple right-hand sides. Block algorithms attempt to accelerate the convergence of iterative Krylov-subspace methods by solving the multiple systems simultaneously. This paper compares a block generalisation of the quasi-minimal residual method (QMR), Block Conjugate Gradient on the normal eq...
متن کامل