## Tridiagonal Matrix Algorithm

version 6.0.1 (254 KB) by
Solves the tridiagonal linear system Ax = d for x using two separate implementations of the tridiagonal matrix algorithm.

Updated 23 Oct 2022

From GitHub

# 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.

• See "EXAMPLES.mlx" or the "Examples" tab on the File Exchange page for examples.

### Cite As

Tamas Kis (2022). Tridiagonal Matrix Algorithm (https://github.com/tamaskis/tridiagonal-MATLAB/releases/tag/v6.0.1), GitHub. Retrieved .

##### MATLAB Release Compatibility
Created with R2021a
Compatible with any release
##### Platform Compatibility
Windows macOS Linux