1SLAE2(1)            LAPACK auxiliary routine (version 3.2)            SLAE2(1)
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NAME

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

10       SUBROUTINE SLAE2( A, B, C, RT1, RT2 )
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12           REAL          A, B, C, RT1, RT2
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PURPOSE

15       SLAE2  computes the eigenvalues of a 2-by-2 symmetric matrix
16          [  A   B  ]
17          [  B   C  ].  On return, RT1 is the eigenvalue  of  larger  absolute
18       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.
38       RT2  may be inaccurate if there is massive cancellation in the determi‐
39       nant A*C-B*B; higher precision or correctly rounded or correctly  trun‐
40       cated  arithmetic  would  be  needed  to  compute RT2 accurately in all
41       cases.
42       Overflow is possible only if RT1 is within a factor of 5  of  overflow.
43       Underflow is harmless if the input data is 0 or exceeds
44          underflow_threshold / macheps.
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48 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                        SLAE2(1)