newtons-method

I am trying to write a function that implements Newton's method in two dimensions and whilst I have done this, I have to now adjust my script so that the input parameters of my function must be f(x) in a column vector, the Jacobian matrix of f(x) , the initial guess x0 and the tolerance where the function f(x) and its Jacobian matrix are in separate .m files. As an example of a script I wrote that implements Newton's method, I have: n=0; %initialize iteration counter eps=1; %initialize error x=[1;1]; %set starting value %Computation loop while eps>1e-10&n<100 g=[x(1)^2+x(2)^3-1;x(1)^4-x(2)^4+x

How many recursions are made before every single root is found? Also, which ones are the roots? Here's my code: e=0.000001; f1=@(x) 14.*x.*exp(x-2)-12.*exp(x-2)-7.*x.^3+20.*x.^2-26.*x+12; a=0; c=3; while abs(c-a)>e b=(c+a)/2; if f1(a)*f1(b)<0 c=b; else a=b; end disp(b); end Bisection works by taking endpoints of some initial interval [a,b] and finding which half of the interval must contain the root (it evaluates the midpoint, and identifies which half has the sign change). Then bisection repeats the process on the identified half. Bisection converges upon only one possible root, and if your

Over the past couple of weeks I've been trying to simulate orbits in a solar system simulation I am making as part of a University module. To cut things short, my simulation is written in C++ using the Ogre3D rendering engine. I have attempted to implement orbits using Newton's law of universal gravitation which made my planet head towards the sun in a straight line, pass through the sun and then come back to its starting position. I also tried the steps from 'Position as a function of time' section of this wikipedia article , but that did not work for me either. I am driving the simulation

I'm working to finish a math problem that approximates the square root of a number using Newton's guess and check method in Python. The user is supposed to enter a number, an initial guess for the number, and how many times they want to check their answer before returning. To make things easier and get to know Python (I've only just started learning the language a couple of months ago) I broke it up into a number of smaller functions; the problem now, though, is that I'm having trouble calling each function and passing the numbers through. Here is my code, with comments to help (each function

Newtons-Raphsons method is easy to implement in Mathematica but in Matlab it seems a bit difficult. I don't get if I can pass a function to a function and how to use the derivative as a function. newtonRaphson[f_, n_, guess_] := If[n == 0, guess, newtonRaphson[f, n - 1, guess - f[guess]/f'[guess]]] newtonRaphsonOptimize[f_, n_, guess_] := If[n == 0, guess, newtonRaphsonOptimize[f, n - 1, guess - f'[guess]/f''[guess]]] It doesn't seem like you can derive neither function-handles nor functions defined in a file but I might be wrong. You could use an implementation like this: function x = newton

I'm reading this document: http://software.intel.com/en-us/articles/interactive-ray-tracing and I stumbled upon these three lines of code: The SIMD version is already quite a bit faster, but we can do better. Intel has added a fast 1/sqrt(x) function to the SSE2 instruction set. The only drawback is that its precision is limited. We need the precision, so we refine it using Newton-Rhapson: __m128 nr = _mm_rsqrt_ps( x ); __m128 muls = _mm_mul_ps( _mm_mul_ps( x, nr ), nr ); result = _mm_mul_ps( _mm_mul_ps( half, nr ), _mm_sub_ps( three, muls ) ); This code assumes the existence of a __m128

I am currently trying to convert colours between RGB (red, green, blue) colour space and RYB (red, yellow, blue) colour space and back again. Based on the details in the following paper, I am able to convert from RYB to RGB using trilinear interpolation - where the parametric weightings (s,t,u) are the RYB colors, and the vertices of the cube are 3d points in RGB space. Paint Inspired Color Mixing and Compositing for Visualisation - Gossett and Chen - Section 2.1 - Realization Details My difficulties are in reversing the conversion process. A second paper references the use of this technique