f02adf

f02adf © Numerical Algorithms Group, 2002.

Purpose

F02ADF All eigenvalues of generalized real symmetric-definite eigenproblem (Black Box)

Synopsis

[r,ifail] = f02adf(a,b<,ifail>)

Description

 
 The problem is reduced to the standard symmetric eigenproblem 
 using Cholesky's method to decompose B into triangular matrices, 
     T                                                         
 B=LL , where L is lower triangular. Then Ax=(lambda)Bx implies 
   -1  -T   T             T                            
 (L  AL  )(L x)=(lambda)(L x); hence the eigenvalues of 
 Ax=(lambda)Bx are those of Py=(lambda)y where P is the symmetric 
         -1  -T                                                
 matrix L  AL  . Householder's method is used to tridiagonalise 
 the matrix P and the eigenvalues are then found using the QL 
 algorithm.

Parameters

f02adf

Required Input Arguments:

a (:,:)                               real
b (:,:)                               real

Optional Input Arguments:                       <Default>

ifail                                 integer  -1

Output Arguments:

r (:)                                 real
ifail                                 integer