made first order actually first order and added fourth order #120
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pavelkomarov
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Jul 1, 2025
| [(-25, -25), (0, 0), (0, 0), (1, 0)], | ||
| [(-25, -25), (-13, -13), (0, 0), (1, 1)], | ||
| [(-25, -25), (0, 0), (0, 0), (1, 1)], | ||
| [(-25, -25), (1, 0), (0, 0), (1, 1)], |
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The first order bounds only get a touch worse when we make first_order truly first order.
pavelkomarov
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Jul 1, 2025
pynumdiff/tests/test_diff_methods.py
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| [(1, 0), (1, 0), (1, 1), (1, 1)], | ||
| [(1, 0), (1, 1), (1, 0), (1, 1)], | ||
| [(2, 2), (3, 2), (2, 2), (3, 2)], | ||
| [(2, 2), (3, 3), (2, 2), (3, 3)]], |
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The "iterated_first_order" bounds get worse all over the place, because the horizontal bias introduced by a non symmetric first-order method causes drift over the iterations.
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The |
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Let's merge this one after #125. I think I'm going to want to make a couple follow-on commits to it. I need to:
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Addressing #104. The resulting
first_orderis biased to one side, resulting in drift when it's iterated:This is likely why you attempted some forward-backward averaging, @florisvb.
Honestly, is it worth keeping around
first_order? My guess is it's not in wide usage, because the higher order methods are equally usable and right there for the taking. Iteratingfirst_ordermight be a thing people do, but in that case they're actually iteratingsecond_order, so we should update the code to reflect that and feed them a warning if they try to callfirst_order.