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Hacker's Guide to Numerical Analysis

356 点作者 bollu大约 4 年前

11 条评论

SavantIdiot大约 4 年前
&quot;It is not transparent to me why this definition is sensible.&quot;<p>Because if I have a six digit meter and I measure 5.0000 volts I know that it is 5.0000 volts. I don&#x27;t see why that is confusing at all.<p>&quot;Here, yyy has correct one and three significant digits relative to xxx, but incorrect 2 significant digits, since the truncation at x2x_2x2 and y2y_2y2 do not agree even to the first significant digit. &quot;<p>This doesn&#x27;t make sense. Y has the correct one?<p>I think you might be confused about the purpose of significant digits. SD are intended to be paired with a tolerance. If there is no tolerence quote with the number, it is meaningless to talk about significant digits. You arbitrarily defined the tolerance as +&#x2F;0.5 (half a unit). That is not always true, almost never true. Consider test equipment, not every multimeter is going to be +&#x2F;0.5mV, some might be +&#x2F;-.3uV. It varies.
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jphoward大约 4 年前
This is such a great example of how people that know math(s) really struggle to explain things to people who don&#x27;t, because they struggle to realise how much lingo they are using.<p>The first point explains something as basic as absolute and relative errors. Great.<p>1 page down (s)he&#x27;s casually thrown in function notation with R representing the real numbers with no explanation. Anyone who isn&#x27;t familiar with this notation is immediately intimidated. But I&#x27;d wager almost anyone who is familiar with it didn&#x27;t need to read the page before it. But also, I think it&#x27;s just unnecessary to be this specific in the first place, if you&#x27;re trying to quickly explain concepts.<p>It&#x27;s actually a huge problem in maths and even Wikipedia (I feel) is pretty guilty of this.<p>If you take a (relatively) key mathematical concept, such as the Taylor series, then the opening gambit is completely incomprehensible to anyone who isn&#x27;t already knowledgeable in maths: <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Taylor_series" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Taylor_series</a><p>This, to me, seems in huge contrast with other scientific fields. Medicine wikipedia, for example, caters towards the &quot;average reader&quot; first, and doctors later. This is entirely appropriate for an encyclopedia. For example: <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;AV_nodal_reentrant_tachycardia#:~:text=AV%2Dnodal%20reentrant%20tachycardia%20(AVNRT,most%20common%20regular%20supraventricular%20tachycardia" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;AV_nodal_reentrant_tachycardia...</a>
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singhrac大约 4 年前
Since it was linked, Herbie will help you find numerically stable versions of your expression: <a href="https:&#x2F;&#x2F;herbie.uwplse.org&#x2F;" rel="nofollow">https:&#x2F;&#x2F;herbie.uwplse.org&#x2F;</a>
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rarefied_tomato大约 4 年前
For a deeper look, Trefethen&#x27;s Numerical Linear Algebra starts with these ideas and applies them to matrix algorithms.
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smlckz大约 4 年前
I am unable to forgive the author for the following:<p><pre><code> #include &lt;cmath&gt; #include &lt;stdio.h&gt; </code></pre> The code looks almost like pure C, but that little `c`...
dennis714大约 4 年前
Shameless plug about IEEE 754 round-off errors: <a href="https:&#x2F;&#x2F;yurichev.com&#x2F;news&#x2F;20210131_IEEE_754&#x2F;" rel="nofollow">https:&#x2F;&#x2F;yurichev.com&#x2F;news&#x2F;20210131_IEEE_754&#x2F;</a>
chrisjharris大约 4 年前
Are there any plans for a physical book? My attention span seems to be calibrated to focus for a prolonged period on paper but less so for information on screen.
omginternets大约 4 年前
I really wanted to be interested in this, but I wish there were more context. When does this kind of stuff come up?
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apbytes大约 4 年前
In the derivation for conditioning what is `O(dx^2)` and why is it there? Looks something like error margin?
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cambalache大约 4 年前
My rule of thumb is that anything title &quot;...for Hackers&quot; is crap.This link was not an exception.<p>&gt; Since the relative error is invariant under scaling (x↦αx)(x \mapsto \alpha x)(x↦αx), we will mostly be interested in relative error.<p>No, No, No, No. This is very much dependent on what you are measuring&#x2F;modelling, what is the tolerance you are willing to accept, the consequences and so on.<p>A 1% of error in the change the cashier gave you back maybe is not a big deal. That same error in the national budget is equivalent to 2X the NASA&#x27;s budget.
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ubavic大约 4 年前
Digression: for all authors that want minimalistic website, please don’t push it too hard, as author of this website did. Color scheme is nice, as is font selection, but it lacks navigation links. Putting simple link to website home would do so much for explorers of site.
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