slae2 (3) - Linux Man Pages
subroutine slae2 (realA, realB, realC, realRT1, realRT2)
SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.
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 is REAL The (1,1) element of the 2-by-2 matrix.
B is REAL The (1,2) and (2,1) elements of the 2-by-2 matrix.
C is REAL The (2,2) element of the 2-by-2 matrix.
RT1 is REAL The eigenvalue of larger absolute value.
RT2 is REAL The eigenvalue of smaller absolute value.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
- 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.
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