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Inverse Algorithms for Matrices Analysis

#0333


Development of the Spectral Method for Analysis of Inverse Algorithms for Ill-Conditional Matrices.

Tech Area / Field

  • OBS-OTH/Other/Other Basic Sciences

Status
8 Project completed

Registration date
05.01.1995

Completion date
26.11.1998

Senior Project Manager
Coevering G van de

Leading Institute
NIIIT (Pulse Techniques), Russia, Moscow

Project summary

Many significant practical problems, particularly those in experimental data processing, can be described as ill-conditioned, i.e., linear transformations which are close to singular. To invert these transformation matrices one employs perse algorithms with extremely narrow limits of validity, and which are based only on computational experience. The goal of this project is to develop as far as possible a uniform method based on a spectral approach which would justify and improve the efficiency of these algorithms.

To evaluate a spectrum, and most particularly its lower module, we will use a new iterative method which is a generalization of /I/ for polynomials with matrix coefficients. It features high stability as regards rounding errors, allows almost full parallellization in computations, and makes it possible to find any isolated modular part of the spectrum without having to find all the eigenvalues.

The project will theoretically and experimentally verify this new method for determining the spectrum of a matrix. The new method will be used to examine one or two algorithms for the inverse of ill-conditioned matrices.

Project duration: Two years. Number of person-years required from former weapons development specialists: five. No auxiliary personnel required.


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