Inversion of Band Matrices

Abstract

This is the summary report for the project entitled Matrix methods for special functions arising in applications. An extremely simple and efficient method for computing the zeros (possibly complex) of Bessel functions J (Z) (sub m) of any real order and of their derivatives was developed and tested. For the complex zeros (the case m < -1) the numerical experiment shows that the method computes the zeros in the increasing order of distance from the origin. The method developed in this project is the first known systematic method for computing the complex zeros of Bessel functions of order less than -1. The method consists of writing the well-known three-term recurrence relations in matrix form, thus reformulating the problem of finding the zeros as eigenvalue problem for infinite matrices. A very complete analysis for the rate of convergence has been obtained for the zeros of Bessel functions of real order greater than -1.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1979
Accession Number
ADA215206

Entities

People

  • Yasuhiko Ikebe

Organizations

  • Northwestern University

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Bessel Functions
  • Classification
  • Computer Science
  • Convergence
  • Eigenvalues
  • Equations
  • Error Analysis
  • Inversion
  • Security
  • Wave Functions

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)