Newton's method Definition and 90 Threads

Hi, guys, I have a questions to ask you about Newton's Method. I knew that Newton's Method was used to estimate the true value of the root of the real number by analysis the graph of that particular function, but I just wonder that do I have to plot the graph of the function everytime I want...

Homework Statement Use Newton's method to find ALL roots of e^x=3-3x Homework Equations The Attempt at a Solution I know how to use Newton's method, but how is it possible to use it to find ALL the roots of the function? Just by looking at the function however, I THINK that...

Homework Statement Use Newton's Method to approximate 96^(1/96) correct to 8 decimal places. Homework Equations Newton's Method equation: Second Approx = (first approx) - (f(first approx))/(f'(first approx)) The Attempt at a Solution So I know that 96^(1/96) must = some number x...

Homework Statement The most commonly used algorithm for computing \sqrt{a} is the recursion xn+1 = 1/2 (xn + a/xn), easily derived by means of Newton's method. Assume that we have available to us a very simple processor which only supports addition, subtraction, multiplication, and halving (a...

1. The problem statement: In what region can we choose x0 and get convergence to the root x = 0 for f(x) = e-1/x^2 Homework Equations xn+1 = xn - f(xn) / f'(xn) The Attempt at a Solution The only thing I've come across is a formula that says |root - initial point| < 1/M where M =...

1. Construct a function f (x) so that Newton's method gets 'hanging' in an infinite cycle xn = (-1)n x0 , no matter how the start value x0 is chosen. 2. Homework Equations : xn+1 = xn - f(xn) / f'(xn) The Attempt at a Solution xn+1 = xn - f(xn) / f'(xn) = (-1)n+1x0 = (-1)nx0 -...

Homework Statement This is problem 2.4.11 from Thomson, Bruckner, and Bruckner, "Elementary Real Analysis." It is from the "Challenging Problems" section of Chapter 2, Sequences. Note that differentiation and continuity have not been covered at this point, but it is presumed that the reader...

Hi all I have these problem on my test review and even after guessing one right I have no idea how one would arrive at that answer so your help is greatly appreciated. Homework Statement 1.find the limit as x approaches 0 in the equation[(3/x^4)-(4/x^2)] 2.Use Newton's method to find the...

Does anyone know of a Newton's method derivative that does not require an inverted Jacobian? I am attempting to port my code from one language to another, and rather than rely on outside libraries for matrix inversions (like I am now), I would prefer to simply do away with the inverted matrix...

Homework Statement The statement \sqrt[4]{a}=x means that x^{n}=a. Using this, we can approximate the radical \sqrt[n]{a} by approximating the solution to the equation x^{n}-a=0. Consider the function f(x)=x^{n}-a. We can use Newton's Method to approximate where f(x)=0 and thus...

Homework Statement "The goal of this task is to check that you understood the derivation of Newton’s method in the lecture. 1. Consider a smooth function G defined from \mathbb{R}^N to \mathbb{R}^N. Suppose it admits a fixed point r \in \mathbb{R}^N. Write down the Taylor development of this...

Homework Statement let x0, x1,... be the approximations of pi from the Newton's Method. Use Mean Value theorem to show that |pi-xj+1|=|tan2cj||pi-xj| for some cj between xj and pi Homework Equations pi is defined as smallest positive number r when sin r =0 The Attempt at a Solution I have...

This is less a homework problem and more conceptual help for a homework problem I have been given the information for a revenue equation and a cost equation I set up Newton's Method with XN+1=\frac{revenue-cost}{the derivative of the top} where both revenue and cost are...

Dear all, Consider the system given by : http://www.freeimagehosting.net/image.php?53f7eed9ce.jpg where we are trying to solve for s and gamma using Newton's method. It turns out to be a simple implementation. Now, what if we need to impose an inequality constraint on the solution s : one...

Homework Statement Hi there. I'm having some trouble with this exercise, which says: Use the Newton's method for determining the zeros of f(x) to 5 decimal places for f(x)=x^5+x-1. So f'(x)=5x^4+1 I thought of iterating till I get x_n-x_{n+1}<0.000001. The thing is that I get to a point where...

Homework Statement Nother Q for today: Let f(x)= (1/x)^x - x (a)show that f(x)=0 has a solution (b)show that there is only one solution to f(x)=0 (c)use Newton's Method to find the second approximation x2 of the solution to f(x) = 0 using the initial approximation x1 = 1/2 Homework...

When using Newton's method to find roots, why should we check that ff'' >0 . I can't find an adequate reason for this. Does Newton's method fail otherwise? If so why? Thanks.

Homework Statement Its not an actual problem, just a question. We're being lectured on Newton's Method, which I understand. But there's a section in the book (and related problems later in the chapter), that ask for you to find (2)^1\6 correct to eight decimal places. It goes on to say that...

Homework Statement Use Newton's method to find the coordinates of the inflection point of the curve y = e^cosx, 0 <= x <= pi, correct to six decimal places. Homework Equations None. The Attempt at a Solution I calculated y'' (as f(x) in Newton formula) and y''' (as f'(x) in...

I understand the rational for using the Lambert W. function for solving equations such as x^x = z , where no derivative in terms of elementary functions exists for the expression. However, on the Wikipedia page about the Lambert W. function, an example is given with the equation 2^t = 5t. In...

I have a situation where I am using Newton's Method to solve a highly nonlinear, non-analytic equation with both positive and negative zeros. My situation requires that only positive zeros be found. Does anyone know any extensions to NM to restrict the solutions to greater than zero? Thanks.

I'm working on a problem where I need to find minimum of a 2D surface. I initially coded up a gradient descent algorithm, and though it works, I had to carefully select a step size (which could be problematic), plus I want it to converge quickly. So, I went through immense pain to derive the...

Greetings, I am trying to implement backward euler implicit method by Newton-raphson iteration. The differential equation is for a simple planar pendulum. So the function for the pendulum is : (1) angularAcceleration (angle) = ( -gravity/length ) * sin(angle); and the update function for...

Homework Statement x_k+1=x_k-(f(x_k)/f'(x_k)), x_0=.5 Homework Equations The Attempt at a Solution Not really a math question, just a computation question. I want to put a do loop around Newton's method using mathlab. x_1=x_0-(f(x_0)/f'(x_0)), x_0=.5,x_2=x_1-(f(x_1)/f'(x_1))...

Homework Statement (i) Use Newton’s Method and apparent convergence to solve x ln(x) = 5 accurate to 3 and 4 significant figures. Start out with x0 = 2. (ii) Directly approximate the absolute error on f, i.e. _f = f(x) − f(˜x). (iii) Use the difference between the 4 significant figures...

Under what circumstances will Newtons method for a system of nonlinear equations converge? Are there any criteria at all which guarantees convergence? Regards

Homework Statement Our assignement is to fix an .m file, which should produce Newton's method for a function. I'm very new to Matlab and some expressions are weird to me. The Attempt at a Solution So I've got the code to look like this: function point=teemuNewton(xbeg, ybeg, iternmbr)...

Homework Statement Find, to three decimal places, the value of x such that e-x = x. Use Newton's method. Homework Equations The Attempt at a Solution I looked up what Newton's method was and I found that it was f(x)= \int x = f(xo) + f](xo)(x-xo) But I don't understand how...

Homework Statement using Newtons method with an initial estimate of x0=2, find the point where the graph f(x)=x3-x-2 crosses the x-axis Homework Equations xi+1 = xi - f(xi)/f'(xi) The Attempt at a Solution Using a function plotter, I know the answer should be around 1.52138...

Homework Statement Find the x-coordinate of the first point in the region where intersects . Give your answer to 6 significant figures. Homework Equations x_1=x_0- (f(x)/f'(x)) The Attempt at a Solution I equated the two equations and got: 0=tanx-5x I also looked at the graph...

I'm working on a program for Newton's method for solving equations. This is my code: ======================================================= program Newton implicit real(a-h,o-z) F(x) = x**2 - 4 !...&---1---------2---------3---------4---------5---------6---------7---...

Hi, I have to describe the famous Newton-rapshon algorithm for finding a root of the function this is what i came up with, i aint not familiar with MATLAB and programming at all, so this is somewhat a melt from a lot of MATLAB tutorials, I don't master the code, but what's really a challenge...

lets say i have the functions f(x,y) = cos(x-y) - y and g(x,y) = sin(x+y) - x. I want to use Newton's method to approximate these functions. Do I just take the partial derivatives with respect to x and y of each function and plug in a given point (a,b)?

Homework Statement Find the coordinates to two decimal places of the point P in Figure 9 where the tangent line to y=cosx passes through the origin. the image is the graph of y=cosx P intersects the graph at around pi. Homework Equations The Attempt at a Solution I don't...

Homework Statement Problem: A (area) = \int^{e}_{1} ln(x) dx = 1 Now we let k be such that 0 \leq k \leq1 Consider the line y = k. Find k so that area computed by A is exactly one half. Homework Equations So, first, I found point of intersection: k = ln (x) e^{k} = x...

Homework Statement Identify the formula x[SIZE="1"]n+1 = -2x[SIZE="1"]n + 3yx[SIZE="1"]n^(2/3) as the Newton's method for a certain function. Here y is a fixed constant. What is the limit of x[SIZE="1"]n? Homework Equations Newton's method?: x[SIZE="1"]n+1 = x[SIZE="1"]n -...

Homework Statement Given two functions; y= ln(x) and y=(x^2)/8 - 2 Use Newton's Method to approximate all intersection points of the given functions, each with 3 decimal places. Homework Equations [SIZE="3"]Xn+1 = [SIZE="3"]Xn - [SIZE="3"]f(x) / f`(x) The Attempt at a Solution...

Hi, I've done something really stupid. I found a Newton's Method program on the internet and copied it to my TI-83 Plus. This program let you put the function in Y1 and its derivative in Y2. Then, you ran the program, and once you input your first guess, you would hit the ENTER key as many times...

i have the answer to this problem i just see why I'm not getting the same answer as my solution manuel. i Have two functtions f(x) = x and g(x) = tan(x) and i have to find where these two functions are equal using Newtons method. i subtracted the two functions to get this new function H(x) =...

Hi everybody, I have a kinda theory to explain but I need a little help to find out the explanation of it. It is, suppose your first guess using Newton's method to find a root is lucky and you guess the exact root of f(x). (Not an approximation,but exact) What happens to your second...