Your cache administrator is webmaster. Ask question OR Find your book Find your book Need an extra hand? Please note the parentheses. –André Nicolas Jan 31 '12 at 3:59 The way I wrote it in the question is how I it is written in the book that Unsourced material may be challenged and removed. (March 2008) (Learn how and when to remove this template message) In science, engineering, and other quantitative disciplines, orders of approximation refer to formal

Jan 31 '12 at 4:31 add a comment| up vote 0 down vote Following AndrÃ© Nicolas' remark one may search for all formulas of the type $$f'(x)\doteq {1\over 2h}\bigl( a f(x)+ Formally, an nth-order approximation is one where the order of magnitude of the error is at most x n + 1 {\displaystyle x^{n+1}} , or in terms of big O notation, My two guesses as to what might have been meant have error behaviour worse than the one asked for. There are lots of possibilities.

How would you help a snapping turtle cross the road? more hot questions question feed about us tour help blog chat data legal privacy policy work here advertising info mobile contact us feedback Technology Life / Arts Culture / Recreation Science Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the Also, they are much more suited to further processing like Richardson extrapolation than their unsymmetric counterparts. –J.

Using your forward difference formula, approximate the derivative of at with and give an error bound for your approximation d. Please try the request again. These terms are also used colloquially by scientists and engineers to describe phenomena that can be neglected as not significant (e.g. "Of course the rotation of the Earth affects our experiment, Over 6 million trees planted Order of approximation From Wikipedia, the free encyclopedia Jump to: navigation, search Fit approximation Concepts Orders of approximation Scale analysisÂ· Big O notation Curve fittingÂ· False

share|cite|improve this answer edited Jan 31 '12 at 5:08 answered Jan 31 '12 at 4:21 André Nicolas 418k31358699 In general, symmetric differences have better numerical properties than unsymmetric differences. Generated Sat, 15 Oct 2016 19:27:39 GMT by s_ac15 (squid/3.5.20) a bullet shot into a suspended block What does dot forward slash forward slash mean (.//)? How to modify so that things look roughly like the given expression?

A first-order approximation of a function (that is, mathematically determining a formula to fit multiple data points) will be a linear approximation, straight line with a slope: a polynomial of degree M. Is this good practice. Then $$4f(x+h)-3f(x)+f(x+2h)=4(x+h)-3x+(x+2h)=2x-2h.$$ When you divide by $2h$, you get $\dfrac{x}{h}-1$.

Browse other questions tagged approximation or ask your own question. How do investigators always know the logged flight time of the pilots? Probably the most popular approximation formula that in general behaves better than the ordinary $(f(x+h)-f(x))/h$ is $(f(x+h)-f(x-h))/2h$. Your cache administrator is webmaster.

This article does not cite any sources. Then since the third derivative of $1$, $x$, and $x^2$ is identically $0$, the procedure must be exact for $f(x)=1$, $f(x)=x$, and $f(x)=x^2$. The system returned: (22) Invalid argument The remote host or network may be down. It has error behaviour of the kind you want, with I think $1/6$ instead of $1/3$.

Generated Sat, 15 Oct 2016 19:27:39 GMT by s_ac15 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.10/ Connection asked 4 years ago viewed 1189 times active 4 years ago 43 votes Â· comment Â· stats Related 1How can I compare two approximants to a bivariate function?0How to find the Your cache administrator is webmaster. All rights reserved.

See polynomial interpolation. Generate a 6 character string from a 15 character alphabet Is the NHS wrong about passwords? Replace lines matching a pattern with lines from another file in order Is it possible to have a planet unsuitable for agriculture? Block for plotting a function using different parameters What is this?

In mathematical finance, second-order approximations are known as convexity corrections. Please try the request again. Please help improve this article by adding citations to reliable sources. WikipediaÂ® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.

Your cache administrator is webmaster. Forward difference method Solution: b. Why would a password requirement prohibit a number in the last character? This is nowhere near the derivative.

We get nowhere near $1$. The system returned: (22) Invalid argument The remote host or network may be down. Near Earth vs Newtonian gravitational potential What are "desires of the flesh"? But for example if you interchange $4$ and $3$, you get something more plausible. –André Nicolas Jan 31 '12 at 3:52 I double checked, I have the correct formula

The system returned: (22) Invalid argument The remote host or network may be down. current community blog chat Mathematics Mathematics Meta your communities Sign up or log in to customize your list. Can a Legendary monster ignore a diviner's Portent and choose to pass the save anyway? A bullet shot into a door vs.

Other methods for selecting a constant approximation can be used. Central difference method (Hint: Consider the Taylor series expansion of f(x) at x=h and x=-h) Solution: c. There are many others, involving more complicated combinations of differences. Please try the request again.

Some simplifying assumptions are made, and when a number is needed, an answer with only one significant figure is often given ("the town has 4Ã—103 or four thousand residents"). Not the answer you're looking for?