# 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

# Descriptors:

# Subject Categories:

- Theoretical Mathematics