Eigenvalues Calculator for a Real Symmetric Matrix

 

This page contains a routine that numerically finds the eigenvalues ONLY of a Real, Symmetric, Matrix. The algorithm is from the EISPACK collection of subroutines.

References:

Smith, B.T.; J.M. Boyle; J.J. Dongarra; B.S. Garbow; Y. Ikebe; V.C. Klema; and C.B. Moler.
          "Matrix Eigensystem Routines--(EISPACK) Guide"
          Springer-Verlag, Berlin.
          1976

Garbow, B.S.; J.M. Boyle; J.J. Dongarra; and C.B. Moler.
          "Matrix Eigensystem Routines--(EISPACK) Guide Extension"
          Springer-Verlag, Berlin.
          1977

The original sub-routines were written in FORTRAN and have been translated to Javascript here. Although all care has been taken to ensure that the sub-routines were translated accurately, some errors may have crept into the translation. These errors are mine; the original FORTRAN routines have been thoroughly tested and work properly. Please report any errors to the webmaster.


HOW TO USE THIS UTILITY

(i) The first entry should be the dimension of the system, N.

(ii) The next N x N entries should be the coefficients of the A Matrix.
The coefficients should be entered in the following order:

a11     a12     a13   . . .
a21     a22     a23   . . .
etc.

Do not enter commas, periods, brackets, etc. Also note that numbers in scientific notation are NOT recognized.

For example, say we want to compute the eigenvalues of a 3 x 3 matrix. Data should be input to the box as follows:

3  
  25     15     -5  
  15     18     0  
  -5     0     11  

Then click the Compute button.

IMPORTANT!
Note the Error Code. If it does not equal 0, some eigenvalues may not have been computed.

 

If Error Code > 0:
If more than 30 iterations are required to determine an eigenvalue, the subroutine terminates. The Error Code gives the index of the eigenvalue for which the failure occurred. Eigenvalues λ 1, λ 2, . . . λ ErCode - 1 should be correct.

 

For more information about this program, see the associated blog post: Eigenvalues Calculator of a Real Symmetric Matrix

 

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