SLAE2(l) — LAPACK auxiliary routine (version 2.0)

NAME

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.