slae2.f(3)

NAME
slae2.f -

SYNOPSIS

  Functions/Subroutines

subroutine slae2 (A, B, C, RT1, RT2)
SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.

Function/Subroutine Documentation

  subroutine slae2 (realA, realB, realC, realRT1, realRT2)

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

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.

Parameters:
    A

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

    B

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

    C

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

    RT1

              RT1 is REAL
              The eigenvalue of larger absolute value.

    RT2

              RT2 is REAL
              The eigenvalue of smaller absolute value.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    September 2012

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 103 of file slae2.f.

Author

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