fixed point iteration and plotting iteration

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I have a map

such that

,

where

is closed unit disc in

and define

where ,

taking

,

i want a matlab code whch calculates

iteration for

in a table format and plots these iteration in

. i will be thankful if someone could help me with it.

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David Goodmanson 2023-9-18

Hi Akansha, the statement x_n+1 = (1-lambda)x_n + lambda x_n appears to be incorrect since the outcome is the uninteresting x_n+1 = x_n. Also, how does T enter into it?

Akansha 2023-9-20

sorry my mistake, iteration is given by x_n+1 = (1-lambda)x_n + lambda T(x_n)

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Answer 1

Voss 2023-9-19

在 MATLAB Online 中打开

0 个投票

Assuming the sequence is defined as in your other question, here's something:

T = @(xy)xy([2 1]).*[-1 1];

n_iterations = 20;

lambda = [0.1 0.2 0.3 0.4];

n_lambda = numel(lambda);

result = cell(1,n_lambda);

for jj = 1:n_lambda

xy = zeros(n_iterations,2);

xy(1,:) = [0.5 1];

for n = 1:n_iterations

xy(n+1,:) = (1-lambda(jj))*xy(n,:) + lambda(jj)*T(xy(n,:));

end

result{jj} = array2table(xy,'VariableNames',{'x','y'},'RowNames',compose('%d',(0:n_iterations).'));

end

figure

hold on

for jj = 1:n_lambda

plot(result{jj}.x,result{jj}.y)

end

legend("lambda = "+lambda,'Location','NorthWest')

result{:}

ans = 21×2 table

x y ________ ________ 0 0.5 1 1 0.35 0.95 2 0.22 0.89 3 0.109 0.823 4 0.0158 0.7516 5 -0.06094 0.67802 6 -0.12265 0.60412 7 -0.1708 0.53145 8 -0.20686 0.46122 9 -0.2323 0.39441 10 -0.24851 0.33174 11 -0.25683 0.27372 12 -0.25852 0.22066 13 -0.25473 0.17274 14 -0.24654 0.13 15 -0.23488 0.092343

ans = 21×2 table

x y _________ _________ 0 0.5 1 1 0.2 0.9 2 -0.02 0.76 3 -0.168 0.604 4 -0.2552 0.4496 5 -0.29408 0.30864 6 -0.29699 0.1881 7 -0.27521 0.091078 8 -0.23839 0.01782 9 -0.19427 -0.033421 10 -0.14873 -0.065591 11 -0.10587 -0.08222 12 -0.068251 -0.08695 13 -0.037211 -0.08321 14 -0.013127 -0.07401 15 0.0043006 -0.061834

ans = 21×2 table

x y _________ _________ 0 0.5 1 1 0.05 0.85 2 -0.22 0.61 3 -0.337 0.361 4 -0.3442 0.1516 5 -0.28642 0.00286 6 -0.20135 -0.083924 7 -0.11577 -0.11915 8 -0.045293 -0.11814 9 0.0037363 -0.096284 10 0.031501 -0.066278 11 0.041934 -0.036944 12 0.040437 -0.013281 13 0.03229 0.0028345 14 0.021753 0.011671 15 0.011726 0.014696

ans = 21×2 table

x y __________ __________ 0 0.5 1 1 -0.1 0.8 2 -0.38 0.44 3 -0.404 0.112 4 -0.2872 -0.0944 5 -0.13456 -0.17152 6 -0.012128 -0.15674 7 0.055418 -0.098893 8 0.072808 -0.037169 9 0.058552 0.0068219 10 0.032402 0.027514 11 0.0084359 0.029469 12 -0.0067262 0.021056 13 -0.012458 0.0099431 14 -0.011452 0.00098262 15 -0.0072643 -0.0039913

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Voss 2023-9-20

You're welcome!

Manahel 2025-5-8

How can I save both the graph and the iteration result tables into a PDF file in MATLAB? Also, where can we find an explanation for each step in the code so we can understand it better

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