Contents

# ?lasd4

Computes the square root of the
i
-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by
?bdsdc
.

## Syntax

Include Files
• mkl.h
Description
The routine computes the square root of the
i
-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix whose entries are given as the squares of the corresponding entries in the array
d
, and that
0 ≤
d
(
i
) <
d
(
j
)
for
i
<
j
and that
rho
> 0
. This is arranged by the calling routine, and is no loss in generality. The rank-one modified system is thus
diag(
d
)*diag(
d
) +
rho
*
Z
*
Z
T
,
where the Euclidean norm of
Z
is equal to 1.The method consists of approximating the rational functions in the secular equation by simpler interpolating rational functions.
Input Parameters
n
The length of all arrays.
i
The index of the eigenvalue to be computed.
1 ≤
i
n
.
d
Array,
DIMENSION
(
n
).
The original eigenvalues. They must be in order,
0 ≤
d
(
i
) <
d
(
j
)
for
i
<
j
.
z
Array,
DIMENSION
(
n
).
The components of the updating vector.
rho
The scalar in the symmetric updating formula.
work
Workspace array,
DIMENSION
(
n
).
If
n
1
,
work
contains (
d
(
j
) +
sigma_i
) in its
j
-th component.
If
n
= 1
, then
work
( 1 ) = 1
.
Output Parameters
delta
Array,
DIMENSION
(
n
).
If
n
1
,
delta
contains (
d
(
j
) -
sigma_i
) in its
j
-th component.
If
n
= 1
, then
delta
(1) = 1
. The vector
delta
contains the information necessary to construct the (singular) eigenvectors.
sigma
The computed
sigma_i
, the
i
-th updated eigenvalue.
info
= 0: successful exit
> 0: If
info
= 1
, the updating process failed.

#### Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.