SLAE2 - compute the eigenvalues of a 2-by-2 symmetric
matrix [ A B ] [ B C ]
SYNOPSIS
SUBROUTINE SLAE2( A, B, C, RT1, RT2 )
REAL A, B, C, RT1, RT2
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.
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.
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