dlae2.f (3) - Linux Manuals
subroutine dlae2 (double precisionA, double precisionB, double precisionC, double precisionRT1, double precisionRT2)
DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.
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.
A is DOUBLE PRECISION The (1,1) element of the 2-by-2 matrix.
B is DOUBLE PRECISION The (1,2) and (2,1) elements of the 2-by-2 matrix.
C is DOUBLE PRECISION The (2,2) element of the 2-by-2 matrix.
RT1 is DOUBLE PRECISION The eigenvalue of larger absolute value.
RT2 is DOUBLE PRECISION 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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