A Capacitance Matrix Method for Dirichlet Problem on Polygon Region.
A Class of Direct Methods for Linear Systems.
A comparison of the accuracy of the finite-difference solution to boundary value problems for the Helmholtz equation obtained by direct and iterative methods
The development of iterative methods for solving linear algebraic equations has brought the question of when the employment of these methods is more advantageous than the use of the direct ones. In the paper, a comparison of the direct and iterative methods is attempted. The methods are applied to solving a certain class of boundary-value problems for elliptic partial differential equations which are used for the numerical modeling of electromagnetic fields in geophysics. The numerical experiments...
A Direct Method for Sparse Least Squares Problems with Lower and Upper Bounds.
A Finite Element - Capacitane Method for Elliptic Problems on Regions Partitioned into Subregions.
A footnote on quaternion block-tridiagonal systems.
A look-ahead algorithm for the solution of general Hankel systems.
A necessary and sufficient criterion to guarantee feasibility of the interval Gaussian algorithm for a class of matrices
A necessary and sufficient to guarantee feasibility of the interval Gaussian algorithms for a class of matrices. We apply the interval Gaussian algorithm to an interval matrix the comparison matrix of which is irreducible and diagonally dominant. We derive a new necessary and sufficient criterion for the feasibility of this method extending a recently given sufficient criterion.
A nested decomposition algorithm for parallel computations of very large sparse systems.
A New Method for the Solution of A x = b.
A Note on Partial Pivoting and Gaussian Elimination.
A note on symplectic block reflectors.
A note on the inversion of Sylvester matrices in control systems.
A parallel algorithm for solving band systems and matrix inversion
A parallel Cholesky algorithm for the solution of symmetric linear systems.
A parallel QR-factorization/solver of quasiseparable matrices.
A remark on cyclic tridiagonal matrices
A remark on Jordan elimination
A stable and optimal complexity solution method for mixed finite element discretizations
A stable and optimal complexity solution method for mixed finite element discretizations
We outline a solution method for mixed finite element discretizations based on dissecting the problem into three separate steps. The first handles the inhomogeneous constraint, the second solves the flux variable from the homogeneous problem, whereas the third step, adjoint to the first, finally gives the Lagrangian multiplier. We concentrate on aspects involved in the first and third step mainly, and advertise a multi-level method that allows for a stable computation of the intermediate and final...