Accurate Semisymbolic Analysis with Usage of 128-bit Arithmetics

Abstract

The semisymbolic analysis generally requires meticulous algorithms from the point of view of accuracy of resulting poles and zeros, especially in the case of huge differences among their absolute values. In the paper, an optimal pivoting strategy is suggested for the algorithm which reduces general eigenvalue problem to the standard one in the case of both full- and sparse-matrix procedures. Using the pivoting, the precision of the poles and zeros increases considerably. However, it is still insufficient for a number of tasks, especially for radio frequency circuits where the poles and zeros are spread over many decades of magnitudes. As contemporary compilers of C++ and Fortran languages have built-in quad precision libraries, it is possible to further enhance the semisymbolic-analysis accuracy using this 128-bit arithmetics.