dlae2(3F)

NAME
     DLAE2 - compute the eigenvalues of a 2-by-2 symmetric matrix  [ A B ]  [
     B C ]

SYNOPSIS
     SUBROUTINE DLAE2( A, B, C, RT1, RT2 )

         DOUBLE        PRECISION A, B, C, RT1, RT2

PURPOSE
     DLAE2  computes the eigenvalues of a 2-by-2 symmetric matrix
        [  A   B  ]
        [  B   C  ].  On return, RT1 is the eigenvalue of larger absolute
     value, and RT2 is the eigenvalue of smaller absolute value.


ARGUMENTS
     A       (input) DOUBLE PRECISION
             The (1,1) element of the 2-by-2 matrix.

     B       (input) DOUBLE PRECISION
             The (1,2) and (2,1) elements of the 2-by-2 matrix.

     C       (input) DOUBLE PRECISION
             The (2,2) element of the 2-by-2 matrix.

     RT1     (output) DOUBLE PRECISION
             The eigenvalue of larger absolute value.

     RT2     (output) DOUBLE PRECISION
             The eigenvalue of smaller absolute value.

FURTHER DETAILS
     RT1 is accurate to a few ulps barring over/underflow.

     RT2 may be inaccurate if there is massive cancellation in the determinant
     A*C-B*B; higher precision or correctly rounded or correctly truncated
     arithmetic would be needed to compute RT2 accurately in all cases.

     Overflow is possible only if RT1 is within a factor of 5 of overflow.
     Underflow is harmless if the input data is 0 or exceeds
        underflow_threshold / macheps.