The index of matrix A in Cn.n is equivalent to the dimension of largest Jor-dan block corresponding to the zero eigenvalue of A. In this paper, indicialequations and normal equations for solving inconsistent singular linear systemof equations are investigated.

In this study, a Taylor method is developed for numerically solving the high-order most general nonlinear Fredholm integro-differential-difference equations in terms of Taylor expansions. The method is based on transferring the equation and conditions into the matrix equations which leads to solve a system of nonlinear algebraic equations with the unknown Taylor coefficients. Also, we test the ...

The transfer-matrix methodology is frequently used to deal with elastic scattering problems that require a solution of the Schrödinger or homogeneous Maxwell equations in the continuous part of their spectra. In its basic formulation, this technique however reveals limited by numerical instabilities, which can be drastically reduced by application of the layer addition algorithm. By providing e...