# ?lae2

Computes the eigenvalues of a 2-by-2 symmetric matrix.

## Syntax

call slae2( a, b, c, rt1, rt2 )

call dlae2( a, b, c, rt1, rt2 )

## Description

The routines sla2/dlae2 compute the eigenvalues of a 2-by-2 symmetric matrix

On return, rt1 is the eigenvalue of larger absolute value, and rt1 is the eigenvalue of smaller absolute value.

## Input Parameters

a, b, c

  REAL for slae2

  DOUBLE PRECISION for dlae2

  The elements a, b, and c of the 2-by-2 matrix above.

## Output Parameters

rt1, rt2

  REAL for slae2

  DOUBLE PRECISION for dlae2

  The computed eigenvalues of larger and smaller absolute value, respectively.

## Application Notes

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.

Parent topic: Auxiliary Routines