Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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.
Complete list of metadatas

https://hal.sorbonne-universite.fr/hal-01083879
Contributor : Thibault Hilaire <>
Submitted on : Wednesday, December 3, 2014 - 9:59:15 AM
Last modification on : Monday, February 10, 2020 - 4:08:10 PM
Document(s) archivé(s) le : Saturday, April 15, 2017 - 1:36:19 AM

File

Article.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01083879, version 1

Citation

Anastasia Volkova, Thibault Hilaire, Christoph Lauter. Reliable evaluation of the Worst-Case Peak Gain matrix in multiple precision. 2014. ⟨hal-01083879v1⟩

Share

Metrics

Record views

64

Files downloads

20