How do I avoid errors due to round-off in Matlab?

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Monisha S R
Monisha S R 2018-10-15
编辑： Bruno Luong 2018-10-15
My code produces round-off errors which I cannot seem to correct even by using vpa(variable). The code gives Nt = 888890 whereas the length(t) = 888889. How do I resolve this discrepancy? I need Nt (number of nodes) to be an integer and the formula for Nt is correct. Any help would be appreciated. Thanks.
dt = 0.0225; tend = 20000;
Nt = round(tend/dt +1);
t = (0:dt:tend)';

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Bruno Luong
Bruno Luong 2018-10-15
t=linspace(0,tend,Nt);
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Bruno Luong
Bruno Luong 2018-10-15
编辑：Bruno Luong 2018-10-15
Because of round-off error as you say. Basically the column syntax increment sequentially from the start value with the given step and go on while the current value <= the specified end value.
Because of round off, it end up slightly larger than 20000 at the step 888890, so this value is not kept.*
Linspace just divides the interval in (n-1) equal parts to get exactly n points, always.
(*) actually there are some special treatment by doing both directions by columns, but for simplicity of the explanation I don't go into the detail of that procedure.
Bruno Luong
Bruno Luong 2018-10-15
编辑：Bruno Luong 2018-10-15
The round-off occurs because 0.0225 = (9/16)*(1/5)*(1/5) and because 1/5 cannot be stored exactly on finite binary, it actually cannot be represented exactly on the computer, so is not 0.0225.
If you try with step for example 0.1250 = 1/8, this problem does not occur, or similar with 0.0625 = 1/16 or 0.03125. I cut my hand if the problem happens with those steps.

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