A Jacobi Type Method for Complex Symmetric Matrices.
A Kaczmarz-Kovarik algorithm for symmetric ill-conditioned matrices.
A least-squares method for the numerical solution of the Dirichlet problem for the elliptic monge − ampère equation in dimension two
We address in this article the computation of the convex solutions of the Dirichlet problem for the real elliptic Monge − Ampère equation for general convex domains in two dimensions. The method we discuss combines a least-squares formulation with a relaxation method. This approach leads to a sequence of Poisson − Dirichlet problems and another sequence of low dimensional algebraic eigenvalue problems of a new type. Mixed finite element approximations with a smoothing procedure are used for the...
A Legendre spectral collocation method for the biharmonic Dirichlet problem
A Legendre Spectral Collocation Method for the Biharmonic Dirichlet Problem
A Legendre spectral collocation method is presented for the solution of the biharmonic Dirichlet problem on a square. The solution and its Laplacian are approximated using the set of basis functions suggested by Shen, which are linear combinations of Legendre polynomials. A Schur complement approach is used to reduce the resulting linear system to one involving the approximation of the Laplacian of the solution on the two vertical sides of the square. The Schur complement system is solved by a...
A linear acceleration row action method for projecting onto subspaces.
A look-ahead algorithm for the solution of general Hankel systems.
A matrix constructive method for the analytic-numerical solution of coupled partial differential systems
In this paper we construct analytic-numerical solutions for initial-boundary value systems related to the equation , where is an arbitrary square complex matrix and ia s matrix such that the real part of the eigenvalues of the matrix is positive. Given an admissible error and a finite domain , and analytic-numerical solution whose error is uniformly upper bounded by in , is constructed.
A method for dealing with ill-conditioned symmetric linear systems
A method for the Eigenreduction of real Symmetric Matrices
A method for the inverse numerical range problem.
A Method of Solving the Stability Problem for Complex Matrices.
A modification of minimal residual iterative method to solve linear systems.
A modification of the two-level algorithm with overcorrection
In this paper we analyse an algorithm which is a modification of the so-called two-level algorithm with overcorrection, published in [2]. We illustrate the efficiency of this algorithm by a model example.
A Modified Bisection Algorithm for the Determination of the Eigenvalues of a Symmetric Tridiagonal Matrix.
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 moving mesh fictitious domain approach for shape optimization problems
A new numerical method based on fictitious domain methods for shape optimization problems governed by the Poisson equation is proposed. The basic idea is to combine the boundary variation technique, in which the mesh is moving during the optimization, and efficient fictitious domain preconditioning in the solution of the (adjoint) state equations. Neumann boundary value problems are solved using an algebraic fictitious domain method. A mixed formulation based on boundary Lagrange multipliers is...
A multigrid algorithm for higher order finite elements on sparse grids.
A Multigrid Method for a Parameter Dependent Problem in Solid Mechanics.
A multigrid method for a Petrov-Galerkin discretization of the Stokes equations.