Provided by: liblapack-doc_3.3.1-1_all

**NAME**

LAPACK-3 - computes 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. LAPACK auxiliary routine (version 3.2) April 2011 SLAE2(3lapack)