summing two 3d matrices to check convergence

Question

Thales 2017-9-5

0
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https://ww2.mathworks.cn/matlabcentral/answers/355258-summing-two-3d-matrices-to-check-convergence

编辑： Matt J 2017-9-5

Given two 3d matrices, obtained in a iterative process as the solution to a PDE, I want to check convergence. To do so, I check:

abs( sum( A(:) - Aold(:) ) ) < eps

Is this the best way to do it? I mean, if I declare

A = rand(100,200,50);
B = rand(100,200,50);

And if I check

check1 = abs( sum( A(:)-B(:) ) );
check2 = abs( sum(sum(sum( A-B ) ) ) );
check3 = abs( sum(A(:)) - sum(B(:)) );
check4 = abs( sum(sum(sum(A))) - sum(sum(sum(B))) );

They should give the same answer. However,

>> check1-check2
ans =
     2.3306e-12
>> check1-check3
ans =
     3.8846e-09
>> check1-check4
ans =
    -2.4812e-10
>> check2-check3
ans =
     3.8823e-09
>> check2-check4
ans =
    -2.5045e-10
>> check3-check4
ans =
    -4.1327e-09

So it clearly is not exactly the same thing. What is the difference between the methods and what is the difference between sum(A(:)) and sum(sum(sum(A))) ? If I want to check convergence on a iterative process, what is the best way to do it?