Accession Number:

ADA128418

Title:

Error-Free Parallel High-Order Convergent Iterative Matrix Inversion Based on p-ADIC Approximation.

Descriptive Note:

Technical rept.,

Corporate Author:

MARYLAND UNIV COLLEGE PARK COMPUTER VISION LAB

Personal Author(s):

Report Date:

1982-11-01

Pagination or Media Count:

22.0

Abstract:

The Newton-Schultz iterative scheme is reformulated in an algebraic setting to compute the exact inverse of a matrix or the solution of a linear system of equations over the ring of integers, with a high order or convergence, by using a finite segment p-adic representation of a rational. This method is divergence-free it starts with the inverse of a given matrix over a finite field called the priming step and then iterates successively to construct, in parallel, the p-adic approximants Hensel Codes of the rational elements of the inverse matrix. The p-adic approximant is then converted back to the equivalent rational using the extended Euclidean algorithm. The method involves only parallel matrix multiplications and complementations and has a quadratic convergence rate. Extension to achieve higher order convergence is straightforward if parallel matrix arithmetic facilities for higher precision operands in a prime base system are available. Author

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE