Previous: dladiv Up: ../lapack-d.html Next: dlaebz

NAME DLAE2 - compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ] SYNOPSIS SUBROUTINE DLAE2( A, B, C, RT1, RT2 ) DOUBLE PRECISION A, B, C, RT1, RT2 PURPOSE 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 abso- lute value. ARGUMENTS A (input) DOUBLE PRECISION The (1,1) entry of the 2-by-2 matrix. B (input) DOUBLE PRECISION The (1,2) and (2,1) entries of the 2-by-2 matrix. C (input) DOUBLE PRECISION The (2,2) entry of the 2-by-2 matrix. RT1 (output) DOUBLE PRECISION The eigenvalue of larger absolute value. RT2 (output) DOUBLE PRECISION 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.