Numerical Methods Trial And Error
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Trial And Error Examples
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Trial And Error Method Formula
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 top How to use trial and trial and error method of problem solving error up vote 1 down vote favorite 1 I am trying to solve the same problem as asked here. In short, I am trying to find the values for which $$8n^2 \lt 64n\,\log_2(n)$$ To find a solution in the real numbers, it involves using the Lambert W function, but as the domain of the functions is limited to the natural numbers this answer suggests "do it numerically". If this means plugging integers into the two functions trial and error method calculator and finding the values for which the inequality holds, how should I approach the selection of the integers? How can I tackle this problem more efficiently than just picking numbers from the air? numerical-methods share|cite|improve this question asked Mar 9 '13 at 10:22 jsj 255314 Try it for few small numbers first, then try to prove it general 'n', or you can try induction! :) –Inceptio Mar 9 '13 at 10:25 add a comment| 3 Answers 3 active oldest votes up vote 3 down vote accepted Simplify $$\tag08n^2<64n\log_2 n$$ to $$\tag1n<8\log_2 n.$$ As the logarithm has sublinear growst, there are at most finitely many $n$ that satisfy $(1)$. More precisely, the derivative of the left hand side in $(1)$ is $1$, that of the right hand side is $ \frac{8}{n\ln 2}$. As this is $<1$ if $n>\frac 8{\ln 2}\approx11.5$ and $>1$ if $n<\frac8{\ln2}$, we expect that $(1)$ holds precisely for $n_1\le n\le n_2$ with integers $n_1<11.5$ and $n_2>11-5$ yet to be determined. Finding $n_1$ is easy: We see that $(0)$ is not satisfied for $n=0$ (right hand side not defined or $=0$, it's a matter of taste), $n=1$ ($8\not<0$), but is satisfied for $n=2$ ($32<128$). Hence $n_1=2$. Now we look for $n_2$, which turns out to be a bit larger. If we substitute $n=2^\alpha$ with $\alpha\in\mathbb R_{\ge0}$, then $(1)$ becomes $2^\alpha<2^3\alpha$ or $$\tag2 2^{\alpha-3}<\al
from GoogleSign inHidden fieldsBooksbooks.google.com - Emphasizing the finite difference approach for solving differential equations, the second edition of Numerical Methods for Engineers and Scientists presents a methodology for systematically constructing individual computer programs. Providing easy access to accurate solutions to complex scientific and...https://books.google.com/books/about/Numerical_Methods_for_Engineers_and_Scie.html?id=VKs7Afjkng4C&utm_source=gb-gplus-shareNumerical Methods for Engineers and Scientists, Second Edition,My libraryHelpAdvanced Book SearchGet print bookNo eBook availableCRC PressAmazon.com - $11.95Barnes&Noble.com - $121.42 and upBooks-A-MillionIndieBoundAll sellers»Get http://math.stackexchange.com/questions/325413/how-to-use-trial-and-error Textbooks on Google PlayRent and save from the world's largest eBookstore. Read, highlight, and take notes, across web, tablet, and phone.Go to Google Play Now »Numerical Methods for Engineers and Scientists, Second Edition,Joe D. Hoffman, Steven FrankelCRC Press, May 31, 2001 - Mathematics https://books.google.com/books?id=VKs7Afjkng4C&pg=PA133&lpg=PA133&dq=numerical+methods+trial+and+error&source=bl&ots=JqeuMksrLR&sig=_KWbfDV7tyBoOJzqveRypECKazs&hl=en&sa=X&ved=0ahUKEwjg2ZuLguTPAhUW8YMKHWSHAIIQ6AEITTAH - 840 pages 4 Reviewshttps://books.google.com/books/about/Numerical_Methods_for_Engineers_and_Scie.html?id=VKs7Afjkng4CEmphasizing the finite difference approach for solving differential equations, the second edition of Numerical Methods for Engineers and Scientists presents a methodology for systematically constructing individual computer programs. Providing easy access to accurate solutions to complex scientific and engineering problems, each chapter begins with objectives, a discussion of a representative application, and an outline of special features, summing up with a list of tasks students should be able to complete after reading the chapter- perfect for use as a study guide or for review. The AIAA Journal calls the book "...a good, solid instructional text on the basic tools of numerical analysis." Preview this book » What people are saying-Write a reviewWe haven't found any reviews in the usual places.Selected pagesTitle PageIndexReferencesContentsInt
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