Solution of system of linear equations with large coefficients in the diagonal
Solvability classes for core problems in matrix total least squares minimization
Linear matrix approximation problems are often solved by the total least squares minimization (TLS). Unfortunately, the TLS solution may not exist in general. The so-called core problem theory brought an insight into this effect. Moreover, it simplified the solvability analysis if is of column rank one by extracting a core problem having always a unique TLS solution. However, if the rank of is larger, the core problem may stay unsolvable in the TLS sense, as shown for the first time by Hnětynková,...
Solving Confluent Vandermonde Systems of Hermite Type.
Solving large-scale quadratic eigenvalue problems with Hamiltonian eigenstructure using a structure-preserving Krylov subspace method.
Solving linear systems with a Levinson-like solver.
Solving systems of two–sided (max, min)–linear equations
A finite iteration method for solving systems of (max, min)-linear equations is presented. The systems have variables on both sides of the equations. The algorithm has polynomial complexity and may be extended to wider classes of equations with a similar structure.
Some algebraic aspects of multigrid methods
Some characterizations of totally nonpositive (totally negative) matrices.
Some comparison theorems for nonnegative splittings of matrices.
Some comparisons of difference schemes on meshes of Shishkin and Bakhvalov type.
Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem
We consider a model eigenvalue problem (EVP) in 1D, with periodic or semi–periodic boundary conditions (BCs). The discretization of this type of EVP by consistent mass finite element methods (FEMs) leads to the generalized matrix EVP Kc = λ M c, where K and M are real, symmetric matrices, with a certain (skew–)circulant structure. In this paper we fix our attention to the use of a quadratic FE–mesh. Explicit expressions for the eigenvalues of the resulting algebraic EVP are established. This leads...
Some Convergent Jacobi-like Procedures for Diagonalising J-Symmetric Matrices.
Some Generalisations of the Theory of Successive Over-Relaxation.
Some inequalities for commutators and an application to spectral variation.
Some iterative Poisson solvers applied to numerical solution of the model fourth-order elliptic problem
The numerical solution of the model fourth-order elliptic boundary value problem in two dimensions is presented. The iterative procedure in which the biharmonic operator is splitted into two Laplace operators is used. After formulating the finite-difference approximation of the procedure, a formula for the evaluation of the transformed iteration vectors is developed. The Jacobi semi-iterative, Richardson and A.D.I. iterative Poisson solvers are applied to compute one transformed iteration vector....
Some New Results on Unsymmetric Successive Overrelaxation Method.
Some -norm convergence results for Jacobi and Gauss-Seidel iterations.
Some parallel procedures for computing the eigenvalues of a real symmetric matrix.
Some remarks on iterative methods for systems of linear equations
Some remarks on the restarted and augmented GMRES method.