It is clear that C is symmetric. However, in order to avoid the solution of two special eigenvalue problems, it is desirable to have a way of forming the transforming matrix A~* in terms of the known matrix A without a previous determination of the eigenvalues and eigenvectors of A. Indeed, this is possible by an iterative process, based on Newton'sâ€¦ (More)

Two standard principles have previously been used in proving that the solution of an elliptic differential equation can be approximated arbitrarily well by replacing the differential equation by a related difference equation on a sufficiently fine net and then solving the corresponding system of linear algebraic equations. First, for the most importantâ€¦ (More)

The solution for a Dirichlet problem on a given plane domain and with given boundary values is usually approximated in numerical computation by its discrete analog defined and determined on an approximating set of net points. It can be proved that the approximation thus obtained converges to the exact solution, when the net becomes denser indefinitely,â€¦ (More)

In the solution methods introduced byDavidenko andGavurin the nonlinear equation is simulated by an initial value problem involving a differential equation. In this paper a related imbedding method has been presented, where a sequence of locally convergent iteration processes produces a global convergence even without any knowledge of a first approximation.â€¦ (More)

1. Abstract. Any finite number m of eigensolutions of a definitely self-adjoint system of ordinary differential equations may be approximated simultaneously to any desired accuracy by an iterative procedure and the solution of an (m X m)matrix eigenvalue equation. If the method is used with rounded numerical values, intermediate purification steps are foundâ€¦ (More)