On numerical solution of arbitrary symmetric linear systems by approximate orthogonalization

On numerical solution of arbitrary symmetric linear systems by approximate orthogonalization

For many important real world problems, after the application of appropriate discretization techniques we can get symmetric and relatively dense linear systems of equations (e.g. those obtained by collocation or projection-like discretization of first kind integral equations). Usually, these systems are rankdefficient and (very) ill-conditioned, thus classical direct or iterative solvers can no...

Numerical solution of linear control systems using interpolation scaling functions

The current paper proposes a technique for the numerical solution of linear control systems.The method is based on Galerkin method, which uses the interpolating scaling functions. For a highly accurate connection between functions and their derivatives, an operational matrix for the derivatives is established to reduce the problem to a set of algebraic equations. Several test problems are given...

Eecient Approximate Solution of Sparse Linear Systems

We consider the problem of approximate solution e x of a linear system Ax = b over the reals, such that kAe x ? bk kbk; for a given ; 0 < < 1: This is one of the most fundamental of all computational problems. Let (A) = kAkkA ?1 k be the condition number of the n n input matrix A. Sparse, diagonally dominant (DD) linear systems appear very frequently in the solution of linear systems associated...

Iterative Solution of Skew-Symmetric Linear Systems

We offer a systematic study of Krylov subspace methods for solving skew-symmetric linear systems. For the method of conjugate gradients we derive a backward stable block decomposition of skew-symmetric tridiagonal matrices and set search directions that satisfy a special relationship, which we call skew-A-conjugacy. Imposing Galerkin conditions, the resulting scheme is equivalent to the CGNE al...

Solution of Fully Fuzzy Linear Systems by ST Method