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lae2 - Man Page

lae2: 2x2 eig, step in steqr, stemr

subroutine dlae2 (a, b, c, rt1, rt2)
DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.
subroutine slae2 (a, b, c, rt1, rt2)
SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.

Detailed Description

Function Documentation

subroutine dlae2 (double precision a, double precision b, double precision c, double precision rt1, double precision rt2)

DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.

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.

Parameters

          A is DOUBLE PRECISION
          The (1,1) element of the 2-by-2 matrix.

          B is DOUBLE PRECISION
          The (1,2) and (2,1) elements of the 2-by-2 matrix.

          C is DOUBLE PRECISION
          The (2,2) element of the 2-by-2 matrix.

RT1

          RT1 is DOUBLE PRECISION
          The eigenvalue of larger absolute value.

RT2

          RT2 is DOUBLE PRECISION
          The eigenvalue of smaller absolute value.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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.

Definition at line 101 of file dlae2.f.

subroutine slae2 (real a, real b, real c, real rt1, real rt2)

SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.