# bandltsol¶

## Purpose¶

Solves the system of equations $$Ax = b$$ for x, where A is a lower triangular banded matrix.

## Format¶

x = bandltsol(b, A)
Parameters: b (KxM matrix) – A (KxN compact form matrix) – x (matrix) – KxM matrix.

## Examples¶

// Create matrix 'A' and right-hand side 'b'
A = { 1 2 0 0,
2 8 1 0,
0 1 5 2,
0 0 2 3 };

b = { 1.3, 2.1, 0.7, 1.8 };

/*
** Create a matrix containing the lower triangular part
** of 'A'
*/
Alower = lowmat(A);

// Create banded matrix from of 'Alower'
Abandlow = band(Alower, 1);

// Solve the system of equations
x = bandltsol(b, Abandlow);


After the code above:

         1  0  0  0         0  1      1.300     1.3            1.3
Alower = 2  8  0  0 Aband = 2  8 x = -0.063 b = 2.1 Alower*x = 2.1
0  1  5  0         1  5      0.153     0.7            0.7
0  0  2  3         2  3      0.498     1.8            1.8


## Remarks¶

A is a lower triangular banded matrix in compact form. See band() for a description of the format of A.

b can have more than one column. If so, $$Ax = b$$ is solved for each column. That is,

$A*x[.,i] = b[.,i];$