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SLAE2(3F)							     SLAE2(3F)

NAME    [Toc]    [Back]

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

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	SLAE2( A, B, C,	RT1, RT2 )

	 REAL	       A, B, C,	RT1, RT2

PURPOSE    [Toc]    [Back]

     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.

ARGUMENTS    [Toc]    [Back]

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

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

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

     RT1     (output) REAL
	     The eigenvalue of larger absolute value.

     RT2     (output) REAL
	     The eigenvalue of smaller absolute	value.

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.
SLAE2(3F)							     SLAE2(3F)

NAME    [Toc]    [Back]

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

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	SLAE2( A, B, C,	RT1, RT2 )

	 REAL	       A, B, C,	RT1, RT2

PURPOSE    [Toc]    [Back]

     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.

ARGUMENTS    [Toc]    [Back]

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

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

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

     RT1     (output) REAL
	     The eigenvalue of larger absolute value.

     RT2     (output) REAL
	     The eigenvalue of smaller absolute	value.

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.


									PPPPaaaaggggeeee 1111
[ Back ]
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