Tridiagonal Matrix Algorithm

Solves the tridiagonal linear system Ax = d for x using two separate implementations of the tridiagonal matrix algorithm.

Tridiagonal Matrix Algorithm

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.