A Bi-CG type iterative method for Drazin-inverse solution of singular inconsistent nonsymmetric linear systems of arbitrary index.
A Class of Iterative Methods for Solving Saddle Point Problems.
A comparison of three algorithms for reducing the profile of a sparse matrix
A hybrid Arnoldi-Faber iterative method for nonsymmetric systems of linear equations.
A modified Cayley transform for the discretized Navier-Stokes equations
This paper is concerned with the problem of computing a small number of eigenvalues of large sparse generalized eigenvalue problems. The matrices arise from mixed finite element discretizations of time dependent equations modelling viscous incompressible flow. The eigenvalues of importance are those with smallest real part and are used to determine the linearized stability of steady states, and could be used in a scheme to detect Hopf bifurcations. We introduce a modified Cayley transform of the...
A nested decomposition algorithm for parallel computations of very large sparse systems.
A network programming approach in solving Darcy's equations by mixed finite-element methods.
A new block triangular preconditioner for three-by-three block saddle-point problem
In this paper, to solve the three-by-three block saddle-point problem, a new block triangular (NBT) preconditioner is established, which can effectively avoid the solving difficulty that the coefficient matrices of linear subsystems are Schur complement matrices when the block preconditioner is applied to the Krylov subspace method. Theoretical analysis shows that the iteration method produced by the NBT preconditioner is unconditionally convergent. Besides, some spectral properties are also discussed....
A note on consecutive ones in a binary matrix.
A note on estimates of diagonal elements of the inverse of diagonally dominant tridiagonal matrices.
A novel parallel algorithm based on the Gram-Schmidt method for tridiagonal linear systems of equations.
A parallel block Lanczos algorithm and its implementation for the evaluation of some eigenvalues of large sparse symmetric matrices on multicomputers
In the present work we describe HPEC (High Performance Eigenvalues Computation), a parallel software package for the evaluation of some eigenvalues of a large sparse symmetric matrix. It implements an efficient and portable Block Lanczos algorithm for distributed memory multicomputers. HPEC is based on basic linear algebra operations for sparse and dense matrices, some of which have been derived by ScaLAPACK library modules. Numerical experiments have been carried out to evaluate HPEC performance...
A parallel GMRES version for general sparse matrices.
A real-valued block conjugate gradient type method for solving complex symmetric linear systems with multiple right-hand sides
We consider solving complex symmetric linear systems with multiple right-hand sides. We assume that the coefficient matrix has indefinite real part and positive definite imaginary part. We propose a new block conjugate gradient type method based on the Schur complement of a certain 2-by-2 real block form. The algorithm of the proposed method consists of building blocks that involve only real arithmetic with real symmetric matrices of the original size. We also present the convergence property of...
A refined unsymmetric Lanczos eigensolver for computing accurate eigentriplets of a real unsymmetric matrix.
A robust and efficient parallel SVD solver based on restarted Lanczos bidiagonalization.
A streaming approach for sparse matrix products and its application in Galerkin multigrid methods.
A tree-based dataflow model for the unsymmetric multifrontal method.
Algorithmique et calculs de complexité pour un solveur de type dissections emboîtées.
All-at-once preconditioning in PDE-constrained optimization
The optimization of functions subject to partial differential equations (PDE) plays an important role in many areas of science and industry. In this paper we introduce the basic concepts of PDE-constrained optimization and show how the all-at-once approach will lead to linear systems in saddle point form. We will discuss implementation details and different boundary conditions. We then show how these system can be solved efficiently and discuss methods and preconditioners also in the case when bound...