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Solving (cyclic) tridiagonal systems

Richard Reuter

Open publisher page 7 citations

Abstract

An APL2 function is presented for solving cyclic tridiagonal and tridiagonal systems of linear equations. Those systems frequently occur in various areas, e. g. interpolation by spline functions, numerical solution of elliptic differential equations, etc.. The function is based on a modification of the cyclic reduction method [1], [2]. Time measurements show impressive speed-ups over the domino ( ) function and the APL2 versions of the Gaussian elimination method, specialized for cyclic tridiagonal and tridiagonal systems.

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What this paper is about

An APL2 function is presented for solving cyclic tridiagonal and tridiagonal systems of linear equations. Those systems frequently occur in various areas, e. g. interpolation by spline functions, numerical solution of elliptic differential equations, etc.. The function is based on a modification of the cyclic reduction method [1], [2]. Time measurements show impressive speed-ups over the domino ( ) function and the APL2 versions of the Gaussian elimination method, specialized for cyclic tridiagonal and tridiagonal systems.

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Available abstract

An APL2 function is presented for solving cyclic tridiagonal and tridiagonal systems of linear equations. Those systems frequently occur in various areas, e. g. interpolation by spline functions, numerical solution of elliptic differential equations, etc.. The function is based on a modification of the cyclic reduction method [1], [2]. Time measurements show impressive speed-ups over the domino ( ) function and the APL2 versions of the Gaussian elimination method, specialized for cyclic tridiagonal and tridiagonal systems.

Key concepts: Tridiagonal matrix, Tridiagonal matrix algorithm, Mathematics, Interpolation (computer graphics), Applied mathematics, Spline interpolation, Generating function, Mathematical analysis

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