Application of the spectral pseudo-inversion to solving Hermitian systems of differential–algebraic equations

A new effective method for solving Hermitian differential–algebraic systems with constant coefficients is proposed and justified. It uses an explicit representation of the solution based on the spectral pseudo-inversion and an expansion of the matrix exponential via Laguerre polynomial series. An approximate solution is obtained by truncating the series. A new bound for the approximate solution error is derived. Results of numerical experiments with systems arising in interconnect analysis of VLSI circuits are presented and discussed.