Reliable evaluation of the Worst-Case Peak Gain matrix in multiple precision
Abstract
The worst-case peak gain (WCPG) of an LTI filter is an important measure for the implementation of signal processing algorithms. It is used in the error propagation analysis for filters, thus a reliable evaluation with controlled precision is required. The WCPG is computed as an infinite sum and has matrix powers in each summand. We propose a direct formula for the lower bound on truncation order of the infinite sum in dependency of desired truncation error. Several multiprecision methods for complex matrix operations are developed and their error analysis performed. We present a multiprecision complex matrix inversion algorithm using Newton-type iteration, along with its error analysis and proof of convergence. A multiprecision matrix powering method is presented. All methods yield a rigorous solution with an absolute error bounded by an a priori given value. The results are illustrated with numerical examples.
Domains
Computer Science [cs] Computer Arithmetic Computer Science [cs] Signal and Image Processing Computer Science [cs] Numerical Analysis [cs.NA] Computer Science [cs] Hardware Architecture [cs.AR] Computer Science [cs] Mathematical Software [cs.MS] Computer Science [cs] Embedded Systems Mathematics [math] Numerical Analysis [math.NA] Mathematics [math] Optimization and Control [math.OC]
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