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Solution of Linear Equations Associated with Tridiagonal Matrix

IP.com Disclosure Number: IPCOM000050696D
Original Publication Date: 1982-Dec-01
Included in the Prior Art Database: 2005-Feb-10
Document File: 2 page(s) / 68K

Publishing Venue

IBM

Related People

Yu, CC: AUTHOR

Abstract

This algorithm provides stable solutions to systems of linear equations with tridiagonal matrix coefficients. Because it requires no pivoting, when combined with APL array operations it provides a very fast solution to the equations.

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Solution of Linear Equations Associated with Tridiagonal Matrix

This algorithm provides stable solutions to systems of linear equations with tridiagonal matrix coefficients. Because it requires no pivoting, when combined with APL array operations it provides a very fast solution to the equations.

Systems of linear equations with tridiagonal matrix coefficients are involved in many one-dimensional simulations, such as thermal and semiconductor device simulations. The Thomas algorithm, which has been used to solve such equations, has an undesirable singularity; when Beta(i) = 0 for any U, the algorithm fails to produce answers and returns with an error message. (See Dale U. von Rosenberg, Methods for the Numerical Solution of Partial Differential Equations, Elsevier Publishing Co., New York, 1969, p. 113.) One of the ways to avoid the problem is by pivoting. However, pivoting reduces execution speed.

The algorithm diagrammed here can be used in an APL program for Schottky barrier diode simulation. It provides stable solutions without pivoting and is extremely fast when used with APL arra;y operations.

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