SLAS2
November 2006
Purpose
SLAS2 computes the singular values of the 2-by-2 matrix
[ F G ]
[ 0 H ].
On return, SSMIN is the smaller singular value and SSMAX is the
larger singular value.
[ F G ]
[ 0 H ].
On return, SSMIN is the smaller singular value and SSMAX is the
larger singular value.
Arguments
| F |
(input) REAL
The (1,1) element of the 2-by-2 matrix.
|
| G |
(input) REAL
The (1,2) element of the 2-by-2 matrix.
|
| H |
(input) REAL
The (2,2) element of the 2-by-2 matrix.
|
| SSMIN |
(output) REAL
The smaller singular value.
|
| SSMAX |
(output) REAL
The larger singular value.
|
Further Details
Barring over/underflow, all output quantities are correct to within
a few units in the last place (ulps), even in the absence of a guard
digit in addition/subtraction.
In IEEE arithmetic, the code works correctly if one matrix element is
infinite.
Overflow will not occur unless the largest singular value itself
overflows, or is within a few ulps of overflow. (On machines with
partial overflow, like the Cray, overflow may occur if the largest
singular value is within a factor of 2 of overflow.)
Underflow is harmless if underflow is gradual. Otherwise, results
may correspond to a matrix modified by perturbations of size near
the underflow threshold.
a few units in the last place (ulps), even in the absence of a guard
digit in addition/subtraction.
In IEEE arithmetic, the code works correctly if one matrix element is
infinite.
Overflow will not occur unless the largest singular value itself
overflows, or is within a few ulps of overflow. (On machines with
partial overflow, like the Cray, overflow may occur if the largest
singular value is within a factor of 2 of overflow.)
Underflow is harmless if underflow is gradual. Otherwise, results
may correspond to a matrix modified by perturbations of size near
the underflow threshold.