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Tridiagonal Matrix Algorithm View Tridiagonal Matrix Algorithm on File Exchange



tridiagonal_matrix

Solves the tridiagonal linear system for using the matrix implementation of the tridiagonal matrix algorithm.

Syntax

x = tridiagonal_matrix(A,d)

Description

x = tridiagonal_matrix(A,d) solves the tridiagonal linear system for , where is a tridiagonal matrix and .



tridiagonal_vector

Solves the tridiagonal linear system for using the vector implementation of the tridiagonal matrix algorithm.

Syntax

x = tridiagonal_vector(a,b,c,d)

Description

x = tridiagonal_vector(a,b,c,d) solves the tridiagonal linear system for , where is a tridiagonal matrix defined using the tridiagonal vectors (, , and ) and where .



Tridiagonal Matrix Convention

For these implementations, I use the following convention for denoting the elements of the tridiagonal matrix :

Most other references have 's ranging from to both in the definition of the tridiagonal matrix and in the algorithm used to solve the corresponding linear system. In this implementation, I have the 's ranging from to ; this makes the algorithm slightly more straightforward to implement.



Examples and Additional Documentation

  • See "EXAMPLES.mlx" or the "Examples" tab on the File Exchange page for examples.
  • See "Tridiagonal_Matrix_Algorithm.pdf" (also included with download) for the technical documentation.