SLAE2
November 2006
Purpose
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 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) REAL
The (1,1) element of the 2-by-2 matrix.
|
| B |
(input) REAL
The (1,2) and (2,1) elements of the 2-by-2 matrix.
|
| C |
(input) REAL
The (2,2) element of the 2-by-2 matrix.
|
| RT1 |
(output) REAL
The eigenvalue of larger absolute value.
|
| RT2 |
(output) REAL
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.
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.