1SLAE2(1)            LAPACK auxiliary routine (version 3.1)            SLAE2(1)
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NAME

6       SLAE2 - the eigenvalues of a 2-by-2 symmetric matrix  [ A B ]  [ B C ]
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SYNOPSIS

9       SUBROUTINE SLAE2( A, B, C, RT1, RT2 )
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11           REAL          A, B, C, RT1, RT2
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PURPOSE

14       SLAE2  computes the eigenvalues of a 2-by-2 symmetric matrix
15          [  A   B  ]
16          [   B    C   ].  On return, RT1 is the eigenvalue of larger absolute
17       value, and RT2 is the eigenvalue of smaller absolute value.
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ARGUMENTS

21       A       (input) REAL
22               The (1,1) element of the 2-by-2 matrix.
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24       B       (input) REAL
25               The (1,2) and (2,1) elements of the 2-by-2 matrix.
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27       C       (input) REAL
28               The (2,2) element of the 2-by-2 matrix.
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30       RT1     (output) REAL
31               The eigenvalue of larger absolute value.
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33       RT2     (output) REAL
34               The eigenvalue of smaller absolute value.
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FURTHER DETAILS

37       RT1 is accurate to a few ulps barring over/underflow.
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39       RT2 may be inaccurate if there is massive cancellation in the  determi‐
40       nant  A*C-B*B; higher precision or correctly rounded or correctly trun‐
41       cated arithmetic would be needed  to  compute  RT2  accurately  in  all
42       cases.
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44       Overflow  is  possible only if RT1 is within a factor of 5 of overflow.
45       Underflow is harmless if the input data is 0 or exceeds
46          underflow_threshold / macheps.
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51 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                        SLAE2(1)