Extension of P-adic Exact Scientific Computational Library (ESCL) to Compute the Exponential of Rational Matrix

Abstract

For the past three years, we have been developing an Exact Scientific Computational Library (ESCL) using p-adic arithmetic. New algorithms have been designed and implemented for matrix operations with rational numbers by representing numerator and denominator with arbitrary length integers, all integers and fractional numbers are represented by p-adic sequences, and all arithmetic calculations are carried out in p-adic domain. In this project, we have worked on: (1) investigating the relation of the length M of p-adic expansion for a rational matrix and the periodicity of a resulted p-adic sequence from arithmetic operation in p-adic field; and extension of the ESCL to compute: (2) the complex rational matrix; (3) the exponential of a rational matrix.

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Document Details

Document Type
Technical Report
Publication Date
Feb 07, 2008
Accession Number
ADA479031

Entities

People

  • Chao Lu

Organizations

  • Towson University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Arithmetic
  • Computational Processes
  • Computations
  • Decomposition
  • Eigenvalues
  • Eigenvectors
  • Floating Point Operations
  • Iterations
  • Numbers
  • Numerical Analysis
  • Periodic Variations
  • Precision
  • Rational Numbers
  • Real Numbers
  • Sequences
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Linear Algebra
  • Technical Research and Report Writing.