subroutine slae2 (A, B, C, RT1, RT2)
SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.
SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.
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.
Parameters:
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.
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
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.
Definition at line 104 of file slae2.f.
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