Using the Variable-Length Arithmetic for an Accurate Poles-Zeros Analysis

Abstract

In the paper, a reduction algorithm for transforming the general eigenvalue problem to the standard one is presented for both classical full-matrix methods and a sparse-matrix technique appropriate for large-scale circuits. An optimal pivoting strategy for the two methods is proposed to increase the precision of the computations. The accuracy of the algorithms is furthermore increased using longer numerical data. First, a ORQJ.GRXEOH precision sparse algorithm is compared with the GRXEOH precision sparse and full-matrix ones. Finally, the application of a suitable multiple-precision arithmetic library is evaluated.