numerical-methods

问题 There is a generic formula Z^N = A(Z)^N+1 + B(Z)^N+1 . This formula is used to convert a given recursive function back to its original explicit form : Recursive Formulas : 1) R(0) = 1, R(n) = (1/3) R(n-1), n = 1, 2, ... 2) P(0) = 1, P(1) = 1/3, P(n) = (4/3) P(n-1) - (1/3) P(n-2), n = 2, 3, ... 3) Q(0) = 1, Q(1) = 1/3, Q(n) = (10/3) Q(n-1) - Q(n-2), n = 2, 3, ... Then, it suggests that "difference formulas" of the form : 2) P(n) = A(1/3^n) + B 3) Q(n) = A(1/3^n) + B * 3^n represent the general

问题 I have about 100,000 numbers that I would like to group together based on dividing by two or increments of two. PS: The increment values may change and the values found in the main array "x" can only be used once. I'm not sure how to check and stop the loop if a number in the "array_all" array has been repeated from the "x" array. See example below Example: x=[9,8,7,6,5,4,3,2,1] I'm trying to get the array_all array to look like this: array_all= [ 9.00000 4.50000 2.25000 8.00000 4.00000 2

问题 Running a python script on different nodes at school using SSH. Each node has 8 cores. I use GNU Screen to be able to detach from a single process. Is it more desirable to: Run several different sessions of screen. Run a single screen process and use & in a bash terminal. Are they equivalent? I am not sure if my experiments are poorly coded and taking an inordinate amount of time (very possible) OR my choice to use 1. is slowing the process down considerably. Thank you! 回答1: With bash I

问题 For a numerical methods class, I need to write a program to evaluate a definite integral with Simpson's composite rule. I already got this far (see below), but my answer is not correct. I am testing the program with f(x)=x, integrated over 0 to 1, for which the outcome should be 0.5. I get 0.78746... etc. I know there is a Simpson's rule available in Scipy, but I really need to write it myself. I suspect there is something wrong with the two loops. I tried "for i in range(1, n, 2)" and "for i

问题 I am currently trying to implement a machine learning algorithm that involves the logistic loss function in MATLAB. Unfortunately, I am having some trouble due to numerical overflow. In general, for a given an input s , the value of the logistic function is: log(1 + exp(s)) and the slope of the logistic loss function is: exp(s)./(1 + exp(s)) = 1./(1 + exp(-s)) In my algorithm, the value of s = X*beta . Here X is a matrix with N data points and P features per data point (i.e. size(X)=[N,P] )

问题 Is there a reasonable numerical library in pure JavaScript? I'd like array-based vectors, matrices, determinate, and matrix inversion. This is only for small problems, not big ones. I'm aware there are choices in Python, Java, C++, or, oh, perhaps FORTRAN, not to mention R. mmm....FORTRAN...... I'd be happily surprised to get basic vector and matrix operations without having to rebuild the wheel or recode from FORTRAN for a day or two. 回答1: Maybe also of interest: http://www.numericjs.com/

问题 I'm attempting a Runge-Kutta implementation for a mass on a spring in Javascript and visualizing it with D3. The purpose is to compare it to Forward Euler and comment on the differences. My FE works fine and plots fine, but the Runge-Kutta is shooting off in a negative direction and never wrapping around. Here's a plunkr with the vis and the code, but I'll add the JS (only for the ODE solvers) too. // *** Functions for ODE Solvers *** // function FEx (x, v, h) { return x + h*v; } function FEv

问题 I'm looking for a simple way to accomplish in Java what MATLAB's fminsearch() does. I don't need to be as general as fminsearch, in my case I only want to find the minimum (function and parameter values at minimum) of a single-variable nonlinear function. I don't know the analytical expression of the function, but I can evaluate it easily. Do you know of a library that performs this, or of an easy algorithm I could re-implement? Note: I saw that apache's common-math seems to have something

问题 Closed . This question is opinion-based. It is not currently accepting answers. Want to improve this question? Update the question so it can be answered with facts and citations by editing this post. Closed 5 years ago . I am running a numerical experiment that requires many iterations. After each iteration, I would like to store the data in a pickle file or pickle-like file in case the program times-out or a data structure becomes tapped. What is the best way to proceed. Here is the skeleton

问题 Closed . This question is opinion-based. It is not currently accepting answers. Want to improve this question? Update the question so it can be answered with facts and citations by editing this post. Closed 5 years ago . I am running a numerical experiment that requires many iterations. After each iteration, I would like to store the data in a pickle file or pickle-like file in case the program times-out or a data structure becomes tapped. What is the best way to proceed. Here is the skeleton