## Developer Reference

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

# ?ptsvx

Uses factorization to compute the solution to the system of linear equations with a symmetric (Hermitian) positive definite tridiagonal coefficient matrix
A
, and provides error bounds on the solution.

## Syntax

Include Files
• mkl.fi
,
lapack.f90
Description
The routine uses the Cholesky factorization
A
=
L*D*L
T
(real)/
A
=
L*D*L
H
(complex) to compute the solution to a real or complex system of linear equations
A*X
=
B
, where
A
is a
n
-by-
n
symmetric or Hermitian positive definite tridiagonal matrix, the columns of matrix
B
are individual right-hand sides, and the columns of
X
are the corresponding solutions.
Error bounds on the solution and a condition estimate are also provided.
The routine
?ptsvx
performs the following steps:
1. If
fact
=
'N'
, the matrix
A
is factored as
A
=
L*D*L
T
(real flavors)/
A
=
L*D*L
H
(complex flavors), where
L
is a unit lower bidiagonal matrix and
D
is diagonal. The factorization can also be regarded as having the form
A
=
U
T
*D*U
(real flavors)/
A
=
U
H
*D*U
(complex flavors).