Enhancement of the semisymbolic analysis precision using the variable-length arithmetic

Abstract

An optimal pivoting strategy for the reduction algorithm transforming the general eigenvalue problem to the standard one is presented for both full- and sparse-matrix techniques. The method increases the precision of the semisymbolic analyses, especially for large-scale circuits. The accuracy of the algorithms is furthermore increased using longer numerical data. First, a long double precision sparse algorithm is compared with the double precision sparse and full-matrix ones. Further, the application of a suitable multiple-precision arithmetic library is evaluated. Finally, the use of longer numerical data to eliminate possible imprecision of the multiple eigenvalues is evaluated.