## Developer Reference

• 2020.2
• 07/15/2020
• Public Content
Contents

# ?lar1v

Computes the (scaled)
r
-th column of the inverse of the submatrix in rows
b1
through
bn
of tridiagonal matrix.

## Syntax

Include Files
• mkl.fi
Description
The routine
?lar1v
computes the (scaled)
r
-th column of the inverse of the submatrix in rows
b1
through
bn
of the tridiagonal matrix
L*D*L
T
-
λ
*
I
. When
λ
is close to an eigenvalue, the computed vector is an accurate eigenvector. Usually,
r
corresponds to the index where the eigenvector is largest in magnitude.
The following steps accomplish this computation :
• Stationary
qd
transform,
L*D*L
T
-
λ
*
I
=
L(+)
*
D(+)
*
L(+)
T
• Progressive
qd
transform,
L*D*L
T
-
λ
*
I
=
U(-)
*
D(-)
*
U(-)
T
,
• Computation of the diagonal elements of the inverse of
L*D*L
T
-
λ
*
I
by combining the above transforms, and choosing
r
as the index where the diagonal of the inverse is (one of the) largest in magnitude.
• Computation of the (scaled)
r
-th column of the inverse using the twisted factorization obtained by combining the top part of the stationary and the bottom part of the progressive transform.
Input Parameters
n
INTEGER
. The order of the matrix
L*D*L