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(30) |
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(31) |
(a) Assign the initial model and the acceptable error
and set the iterative number k=1.
(b) Calculate and
.
(c) If , then stop iteration; otherwise,
.
(d) Starting from , carry out 1D searching along the searching direction
for
satisfying
.
(e) Letting and k:=k+1, go to step (b).
If the Hessian
is not positive definite, the Newton algorithm should be modified further. That means
is replaced with
. If the
is chosen suitably, the matrix
will be positive definite.
[B] Quasi-Newton algorithm:
The main feature of this algorithm is that the inverse of the Hessian matrix is not explicitly calculated. Further implementing the differential operation on both sides of equation (30) yields
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(32) |
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(33) |
(a) Assign the initial model and the acceptable error
.
(b) Setting H1=In and the iterative number k=1, calculate .
(c) Let .
(d) Starting from , carry out 1D searching along the searching direction
for
satisfying
.
(e) If , then stop iteration; otherwise, go to Step (f).
(f) If k=n, then let , go to Step(b); Otherwise, go to Step (g).
(g) Letting ,
and
, calculate Hk+1 with any of Formula 1-4. Setting k:=k+1, go to Step (c).