numerical-methods

I wish to solve the Lorentz model in Python without the help of a package and my codes seems not to work to my expectation. I do not know why I am not getting the expected results and Lorentz attractor. The main problem I guess is related to how to store the various values for the solution of x,y and z respectively.Below are my codes for the Runge-Kutta 45 for the Lorentz model with 3D plot of solutions: import numpy as np import matplotlib.pyplot as plt #from scipy.integrate import odeint #a) Defining the Runge-Kutta45 method def fx(x,y,z,t): dxdt=sigma*(y-z) return dxdt def fy(x,y,z,t): dydt

I would like to implement the Power Method for determining the dominant eigenvalue and eigenvector of a matrix in MATLAB. Here's what I wrote so far: %function to implement power method to compute dominant %eigenvalue/eigenevctor function [m,y_final]=power_method(A,x); m=0; n=length(x); y_final=zeros(n,1); y_final=x; tol=1e-3; while(1) mold=m; y_final=A*y_final; m=max(y_final); y_final=y_final/m; if (m-mold)<tol break; end end end With the above code, here is a numerical example: A=[1 1 -2;-1 2 1; 0 1 -1] A = 1 1 -2 -1 2 1 0 1 -1 >> x=[1 1 1]; >> x=x'; >> [m,y_final]=power_method(A,x); >> A*x

I need to find the machine epsilon and I am doing the following: eps = 1; while 1.0 + eps > 1.0 do eps = eps /2; end However, it shows me this: Undefined function or variable 'do'. Error in epsilon (line 3) while 1.0 + eps > 1.0 do What should I do? rayryeng First and foremost, there is no such thing as a do keyword in MATLAB, so eliminate that from your code. Also, don't use eps as an actual variable. This is a pre-defined function in MATLAB that calculates machine epsilon , which is also what you are trying to calculate. By creating a variable called eps , you would shadow over the actual

I'm trying to implement the Jacobi iteration in MATLAB but am unable to get it to converge. I have looked online and elsewhere for working code for comparison but am unable to find any that is something similar to my code and still works. Here is what I have: function x = Jacobi(A,b,tol,maxiter) n = size(A,1); xp = zeros(n,1); x = zeros(n,1); k=0; % number of steps while(k<=maxiter) k=k+1; for i=1:n xp(i) = 1/A(i,i)*(b(i) - A(i,1:i-1)*x(1:i-1) - A(i,i+1:n)*x(i+1:n)); end err = norm(A*xp-b); if(err<tol) x=xp; break; end x=xp; end This just blows up no matter what A and b I use. It's probably a

Is there any sparse matrix library that can do these: solve linear algebraic equations support operations like matrix-matrix/number multiplication/addition/subtraction,matrix transposition, get a row/column of a matrix,and so on matrix size could be 40k*40k or bigger,like 250k*250k fast can be used in Windows Can someone recommend some libraries for me? If you recommend, please tell me the advantages and disadvantages of it, and the reason why you recommend it. By the way,I have searched many sparse matrix libraries on the internet and tested some of them. I found that each of them only

Suppose you have an arbitrary triangle with vertices A , B , and C . This paper (section 4.2) says that you can generate a random point, P , uniformly from within triangle ABC by the following convex combination of the vertices: P = (1 - sqrt(r1)) * A + (sqrt(r1) * (1 - r2)) * B + (sqrt(r1) * r2) * C where r1 and r2 are uniformly drawn from [0, 1] , and sqrt is the square root function. How do you justify that the sampled points that are uniformly distributed within triangle ABC ? EDIT As pointed out in a comment on the mathoverflow question , Graphical Gems discusses this algorithm . You have