man dlae2 (Fonctions bibliothèques) - compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ]
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 absolute value.
ARGUMENTS
- A (input) DOUBLE PRECISION
- The (1,1) element of the 2-by-2 matrix.
- B (input) DOUBLE PRECISION
- The (1,2) and (2,1) elements of the 2-by-2 matrix.
- C (input) DOUBLE PRECISION
- The (2,2) element 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.