How to make a composite trapezoidal rule have more than 1 iteration?

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Natalia Wong 2015-12-23

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评论： Walter Roberson 2016-1-11

Hi I have written the function for composite trapezoidal rule and I'm required to calculate the volume by integrating 1/(1+x^2) from 0 to 1. I've found the volume (0.7845) but how do i show the number of iterations and absolute error only when the accuracy of the estimation has improved by a decimal place. I'm supposed to fprintf like the as shown below but i don't understand how to make the trapezoidal rule have more than one iteration??

Thanks I'm new to matlab

Iter Pts    Vol_est    Error
   3   0.41333333 0.05545687 (1 DP)
   6   0.41799014 0.00888872 (2 DP)
 16   0.41878025 0.00098765 (3 DP)
 49   0.41886937 0.00009645 (4 DP)

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Answer 1

Walter Roberson 2015-12-23

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The trapazoidal rule gets more accurate as you sample more finely. The "Iterations" is the number of pieces the range is subdivided in to. 2 pieces takes 3 points, one at the beginning, one in the middle, one in the end. 3 pieces takes 4 points, one at the beginning, one 1/3 of the way, one 2/3 of the way, one at the end. Notice in the table that Pts is always 1 greater than Iter: that is due to this relationship. "Iter" == "Subdivisions"

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Natalia Wong 2015-12-24

Thanks Walter but I only need to display the no. of iterations only if the error has improved by a decimal points. How do I check if my error has improved by a decimal point? Is there a built in function?