Taylor Series for e^x with while loop

Question

Clare Dubecky 2020-10-2

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回答： Sulaymon Eshkabilov 2020-10-3

I am attempting to write a code that will use a while loop to add terms of a taylor series approximation for e^x to a return value called "sum". I am trying to get the while loop to continue until the value of sum does not change after adding a new term. My main question is what term could I use to start the while loop? Should I have it be

while sum(i) ~= sum(i - 1)
end

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James Tursa 2020-10-2

编辑：James Tursa 2020-10-3

Best to use a different variable name than sum, since sum is a standard MATLAB function. E.g., mysum.

Just give mysum(1) and mysum(2) the first two sums of the Taylor series and start i at 2.

That being said, you will not get good results with this as x gets larger, particularly when negative. The intermediate terms can grow hugely before the factorial in the denominator starts to dominate and the terms settle down. In the meantime you will get large cancellation errors in the intermediate sums.

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Answer 1

Sulaymon Eshkabilov 2020-10-3

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在 MATLAB Online 中打开

x = 1.5;        
SUM = 0;
ANS = exp(x);
Err = ANS-SUM;
Err_Margin = 1e-9;
ii=0;
while Err > Err_margin
    ii=ii+1;
    SUM(ii+1) = SUM(ii)+...
    ERR  = ANS-SUM(ii+1);   
end