Numerical analysis Definition and 116 Threads

Let g(x)=(x-x1)(x-x2)(x-x3) -1<=x1<x2<x3<=1 find the points x1,x2,x3 so that max |g(x)| for x an element of [-1,1] is as small as possible. This is the only problem I have left and I have no idea how to do it. We've been covering Newtons method and rootfinding but I don't think it...

Do you know of code (preferably C/C++) to do this for non linear least squares? i found a program called levmar on the internet, but it seems inadequately documented on how to use it and probably not so useful to my purposes. My problem is evaluation of a carpet. The middle is worn out and it...

[SIZE="5"]2 Questions

This is for a computer project and the questions asks to compute a sum from J=1 to n of 1/j^2 from smallest to largest... i.e. (1/n^2+ 1/(n-1)^2+...1/9+1/4+1) for n=10, n=100, n=1000, n=10000, and n=100000 Is there i way i can do this in my calculator? or is there i command i can use in maple??

Homework Statement Consider a symmetric matrix, A, n x n with distinct eigenvalues lambda_1 > lambda_2 > ... > lambda_n (note: i didnt miss anything here typing this, there are no absolute values here). What value of the shift beta will give fastest convergence to lamba_1 and its...

Can you tell me what Numerical Analysis is? I wonder if this is good for a Physics major to take?

using composite trapezoidal rule with n=4 how can i get a bound for the error of I=integration tan(x) from x=0 to x=pi/2 i know that the term of error in comp trapezoidal rule is (b-a)/12 h^2 f''(eita) i got the second derevative of tanx to be 2sec^2 x tanx then i don't know with what value...

in Newton forward differece method. how can i know that i reached the best interpolation? for example in a function like sqrt(x) for Xi=1,1.05,1.10,1.15,1.20,1.25,1.3 the best interpolation is at P3(x) why?how can i know? this really makes me conused:confused: :confused: if anyone...

Hello, I'm trying to construct a code in determining the Asymptotic Error Constant and the order of the rate of convergence, r for several iterative methods like the Fixed point, Newton Rhapson, and Secant methods in determining roots, using Scilab 4.0 (which is said to behave much like...

(I am not sure whether I'm posting in the right forum. I apologize if I do) Does anyone have an alrorithm or a code (in any language) that constructs a Poincare surface of section? I want to do so for a Hamiltonian model: A mass under the influense of the Henon-Heiles potential. It has to...

Consider the fixed point iteration formula: *x_(n+1) = (2/3)[(x_n)^3 - 1] - 3(x_n)^2 + 4x_n = g(x) *Note: "_" precedes a subscript and "^" precedes a superscript (a) Find an interval in which every starting point x_0 will definitely converge to alpha = 1. (b) Show that the order of the...

Hello there! yet another proof, that i need help on I am supposed to prove that the following statement holds for the secant method dk+1/ek -> -1 for k->Infinity where dk+1 is the next change and ek is the error. I have this idea, but i want to hear whether its a valid proof. i use...

Here are my questions: "Evaluating the summation as i goes from 1 to n of a sub i in floating point arithemetic may lead to an arbirarily large error. If however, all summands a sub i are of the same sign, then this relative error is bounded. Derive a crude bound for this error, disregarding...

hello all I have been researching into numerical analysis, differential equations in particular, I underdstand how the Runge kutta methods work geometrically but I don't quit understand what is the idea behind Adam moultons method And Adam Bashforth method, Is there a graphical way of...

I'm need to use Microsoft Excel as a numerical analysis tool for classical mechanics physics problems. Yes, I know there are dozens or hundreds of other tools that would be more powerful, but I (and my students) are required to see what they can do with Excel. The Class: Analytical...

I'll be taking Numerical Analysis in the fall and I honestly have no idea what it's about. Can anyone tell me what the main topics in Numerical Analysis Are? Thanks.