Solution bounds for some strictly diagonally dominant symmetric matrix equations

摘要

Passive resistive circuit models are used to derive bounds for the solution of strictly diagonally dominant symmetric systems of algebraic equations with all of the off-diagonal entries being of the same sign and all diagonal and right-hand side entries being of opposite sign. The values of the unknowns are in an interval obtained from [0,1] by performing an appropriate scaling of the right-hand side entries. This bound interval indicates how to choose the initial guess for an efficient iterative solution of the systems considered.