Problem 45854. Least Absolute Deviations (L1-norm) line fit - degree n

Created by jmac

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This is a generalization of Problem 45851 for degree n
<https://www.mathworks.com/matlabcentral/cody/problems/45851-least-absolute-deviations-l1-norm-line-fit-degree-1>
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You are given two vectors X and Y (coordinates of observations on a plane), and a degree d of the underlying model. Return a row vector P with the d+1 coefficients of the best-fit polynomial, in the L1-norm sense. I.e., find P of degree d that minimizes sum( abs( Y - polyval(P,X) ) ) .
(compare your results with polyfit on the test suite!)

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Last Solution submitted on Apr 17, 2021

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Rafael S.T. Vieira on 18 Sep 2020

The problem with L1-norm is that It may have more than one possible solution. And the test suite should probably take this into account. (And the test suite also needs some fixing.)

PS: It's probably why people usually prefer the L2-norm instead of L1,L3 or LN-norm.

Are Mjaavatten on 17 Apr 2021

In Test 3, input variable d is set to 3 but left out in the call to LADfit. Thus is probably an oversight.

goc3 on 19 Apr 2021

@Are Mjaavatten: the function call in test 3 has been fixed to include all three inputs.

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Problem 45854. Least Absolute Deviations (L1-norm) line fit - degree n

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Problem 45854. Least Absolute Deviations (L1-norm) line fit - degree n

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