|
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(18.17) |
As we know that for ,
, for
not too small we can use
as a starting value for the fixed point iteration
For smaller , we first solve (18.19) for a larger
and then take
as a starting value for (18.20); as a criterium whether (18.20) converges or
not we take the development of the size of
which is controlled by the parameter
expl, the stepsize from
to
is controlled by fact.
Once we have determined for given
, we control whether
is smaller or
larger than
. To determine the pair
for given
, we
use a bisection algorithm, as
is strictly dicreasing in
.
We write
as
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(18.21) |
Now we have to solve
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(18.24) |
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(18.25) |
quantlet | input | output | function |
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(A0,FI,b,N, | (A,V,ctrl) | Fixed-Point-Iteration (18.20) |
eps,itmax, | for sim. clipping; also decides | ||
expl) | if there was convergence or not | ||
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(A0,S1,S2,b, | (A,V,ctrl) | Fixed-Point-Iteration (18.20) |
N,eps,itmax, | for sep. clipping; also decides | ||
expl) | if there was convergence or not | ||
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(aIh, b, N) | (r,s) | ![]() |
Romberg-integration | |||
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(aIh, b, N) | (r,s) | ![]() |
Romberg-integration | |||
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(aIh, b, N) | (r,s) | ![]() |
MC-integration | |||
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(aIh, b, N) | (r,s) | ![]() |
MC-integration | |||
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(c,n) | y | calculates ![]() |
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(c,n) | y | calculates ![]() |
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(t,n) | y | calculates
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(t,n) | y | calculates
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(t,n) | y | calculates
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(t,n) | y | calculates
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