Eigenvalues of a General Matrix

This program computes the eigenvalues of a general matrix (either symmetrical or non-symmetrical).

Given AX= X,

we have the determinant: {A -lamda*1}
as the characteristic polynomial. If the elements of matrix A are real, then the roots of the polynomial
will be real and/or conjugate complex.,  The method presented here was developed by Rutishauser, and is quite good for systems up to N = 30 or 40 when used with computers accurate to 10-15 digits.

Program Notes:

The dimensions of the computer system are limited by the dimension statement at line 40. The system size may be altered as follows:

DIM A(N,N), L(N,N), U(N,N) ,   where N is the maximum size desired,
 

Example
Compute the eigenvalues of the following general matrix:

Downloads;

Basic Program - liberty basic - lbegm.bas

Test Case (above example):

EIGENVALUES OF A GENERAL MATRIX

KEY IN ORDER OF MATRIX 3

INPUT ELEMENTS OF MATRIX A

A(1, 1) =?-1
A(1, 2) =?16
A(1, 3) =?-20

A(2, 1) =?1
A(2, 2) =?0
A(2, 3) =?0

A(3, 1) =?0
A(3, 2) =?1
A(3, 3) =?0


RUNNING
NUMBER OF CYCLES COMPLETED = 47

ELEMENTS OF UPPER TRIANGULAR MATRIX

-5.0
2.04229607
1.95857988