Abstract :
The measure of a matrix is used to, first, bound solutions of ordinary differential equations, bound the computer solution by the backward Euler method, and bound the accumulated truncation error; second, to give conditions for the existence and uniqueness of a dc operating point; third, to determine a convergence region for the Newton-Raphson technique and establish its convergence properties. The unifying idea of the paper is the use of the measure of a matrix.
Keywords :
Computer-aided circuit analysis; Computer-aided circuit design; Matrix methods; Newton-Raphson methods; Nonlinear differential equations; Nonlinear networks; Numerical methods; Algorithm design and analysis; Circuit analysis computing; Computer errors; Computer networks; Convergence; Differential equations; Finite wordlength effects; Helium; Laboratories; Transient response;
