SLAE2  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.

A

          A is REAL


          The (1,1) element of the 2-by-2 matrix.

B

          B is REAL


          The (1,2) and (2,1) elements of the 2-by-2 matrix.

C

          C is REAL


          The (2,2) element of the 2-by-2 matrix.

RT1

          RT1 is REAL


          The eigenvalue of larger absolute value.

RT2

          RT2 is REAL


          The eigenvalue of smaller absolute value.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

September 2012

  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.