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)

Returns:

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,

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