## Developer Reference

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

# ?trnlsp_solve

Solves a nonlinear least squares problem using the TR algorithm.

## Syntax

Include Files
• Fortran:
mkl_rci.fi
,
mkl_rci.f90
Description
The
?trnlsp_solve
routine uses the TR algorithm to solve nonlinear least squares problems.
The problem is stated as follows: where
• F
(
x
):
R
n
R
m
• m
n
From a current point
x
current
, the algorithm uses the trust-region approach: to get
x
new
=
x
current
+
s
that satisfies where
• J
(
x
)
is the Jacobian matrix
• s
is the trial step
• ||
s
||
2
≤ Δ
current
The
RCI_Request
RCI_Request
Value
Description
2
Request to calculate the Jacobian matrix and put the result into
fjac
1
Request to recalculate the function at vector
X
and put the result into
fvec
0
One successful iteration step on the current trust-region radius (that does not mean that the value of
x
has changed)
-1
The algorithm has exceeded the maximum number of iterations
-2
Δ <
eps
(1)
-3
||
F
(
x
)||
2
<
eps
(2)
-4
The Jacobian matrix is singular.
||
J
(
x
)
(1:
m
,
j
)
||
2
<
eps
(3)
,
j
= 1, ...,
n
-5
||
s
||
2
<
eps
(4)
-6
||
F
(
x
)||
2
- ||
F
(
x
) -
J
(
x
)
s
||
2
<
eps
(5)
Note:
• J
(
x
)
is the Jacobian matrix.
• Δ
is the trust-region area.
• F
(
x
)
is the value of the functional.
• s
is the trial step.
Input Parameters
handle
Type
INTEGER*8
.
fvec
REAL
for
strnlsp_solve
DOUBLE PRECISION
for
dtrnlsp_solve