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Algorithms which solve mathematical problems by means of numerical approximation (as opposed to symbolic computation).

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I'm implementing a numerical solver for the 1D diffusion (heat) equation using an iterative method. The initial temperature distribution is a Gaussian profile, which should theoretically smooth out ...
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I'm working on a Java assignment where I must implement the cosine function using only basic arithmetic operations (addition, subtraction, multiplication, division) and no built-in math functions, ...
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I am working with a mechanical system that has five degrees of freedom (a composite plate), and I am trying to compute its frequency response, time-domain response, and natural frequencies. I have ...
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I have written a code that performs numerical integrations—one using the Gauss method and the other using the trapezoidal method. For the Gauss method, I have five separate text files containing the ...
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I've written a Python script to solve a system of coupled differential equations and then use the results to solve an eigenvalue problem. The full problem is: \$\frac{d^2}{dr^2} K(r) = \frac{K(r)}{r^2}...
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I have written a N-body simulator in Rust implementing Barnes Hut algorithm and Leapfrog integrator. My code seems to work fine, but I'd like to review on techniques which can improve performance ...
epestr's user avatar
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I have implemented the Preconditioned Conjugate Gradient (PCG) method for solving a system of linear equations in Python and I would appreciate it if someone could verify its correctness since I am ...
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Please review this C++ listing of an implementation of Leapfrog integration. Was the algorithm implemented correctly? ...
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I am currently working on testing some codes on python to solve differential equations by finite differences, but some problems and equations i am dealing with are: Too big to keep manually writing ...
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This is a toy problem. I want to try using Rust for numerical modeling, but I found zero tutorials for this kind of stuff. I also just started learning Rust yesterday, so please bear with me. Usually ...
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I want to perform some calculations on a large dataset. The code can be found below, where I want to calculate the values for 'results_nr' over a large loop (1000 x 910) values. Can you help me out ...
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I would like to parallelise with OpenMP a one-dimensional integral using the integrate() function implemented in the Boost library. I found a rather obscure ...
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I am trying to speed up as much a possible this function in C++. As I explained in another post, Implementing multidimensional integral for a custom function in C++, this function will be used inside ...
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I'm trying to find the square root of a number (num) using binary search in Rust. I'm new to Rust, but I've done quite a bit of programming in other languages, ...
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I am not an expert with C++, but I am trying to implement a 4-dimensional integral using GSL numerical integration approach. The code below shows the whole algorithm. Although it seems correct what I ...
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I have created an algorithm which calculates the value of PI in JavaScript. Can this algorithm to be improved? ...
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I am learning JavaScript and decided to translate my Python scripts into JavaScript. Approximations of π are extremely popular programming challenges and I am sure they must be a staple of the ...
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Are there any thing that I have to consider to improve the following code in either performance and others? Any comments and suggestions are welcome! ...
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I have realized that all the digital filters of the IIR type have the same structure. They are described by difference equation in following form: $$ y(k) = b_0\cdot x(k) + b_1\cdot x(k-1) + \ldots +...
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I have written a program in C++ that processes financial bond mathematics, making extensive use of the valarray class, so that mathematical functions and operations ...
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I have tried my hand with implementing simple quadrature formulas in C++. Definite integral: $$\int_a^b f(x) dx$$ Domain of integration \$[a, b]\$ divided into \$n\$ intervals of equal length \$h = (b ...
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The most famous library for Support Vector Machine (SVM) algorithm is libsvm (https://github.com/cjlin1/libsvm/), but I felt that its code style is too old, I rewrote in newer C++ as a hobby project. ...
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I wrote a simple linear/polynomial regressor based on my previous matrix project (https://github.com/frozenca/Ndim-Matrix). ...
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I just asked this question over Stack Over Flow on how to improve my code and reposting it here as someone on Stack Overflow recommended this platform. I have written two python functions and they are ...
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I'm trying to perform a 4-dimensional numerical integration in R using a function I wrote in C++ code which is then sourced in <...
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This is a follow-up question for Two dimensional bicubic interpolation implementation in Matlab and Two dimensional gaussian image generator in C. Besides the Matlab version code, I am attempting to ...
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I am attempting to implement two dimensional bicubic interpolation algorithm in Matlab. The input is a two dimensional array and the output is the interpolated result. The test input matrix: ...
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I have tried to code a genetic algorithm to guess the coefficients of a degree 4 polynomial. The information initially provided is values of y = f(x) for different x using the original polynomial. I ...
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(See the previous version here.) This time, I have encorporated all the suggestions made by Marc. Also, I changed the type of points from Double to ...
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(See the previous version here.) (See the next version here.) This time, I have incorporated all the suggestions made by Roman; my new version follows. ...
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I recently needed to create a function to approximate a complex trigonometric function on an embedded system without a floating point unit and without a fast trigonometric library. So I pulled out my ...
Edward's user avatar
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3 answers
316 views

This is an algorithm regarding the RKF method: ...
Amirhossein Rezaei's user avatar
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1 answer
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I have a system of n oscillators which oscillate with time. To each of these oscillators I am adding a fluctuating coloured noise term with a different seed for each oscillator. Here is my code for ...
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I am trying to implement the Euler–Maruyama method and use it to solve the Ornstein–Uhlenbeck process. I am basing my code on the wikipedia page where a python implementation is shown. More generally ...
Iwan Phillips's user avatar
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4 votes
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I've written bounded spigot algorithms(Spigot Algorithm) for e and pi. I would like to understand if there is anything I can do to make this more efficient. I've done things already like move the ...
FodderOverflow's user avatar
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I have a simple task as part of a larger autocorrelation DSP system - to convert from signed 16-bit integer audio samples to floating-point. This part is quite self-contained: ...
Reinderien's user avatar
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This is my first modeling exercise on the particle flow. Recently, I read a paper https://acp.copernicus.org/articles/20/3181/2020/. After reading the paper, thought of modeling it in Python. It seems ...
Vishal's user avatar
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I implemented binary logistic regression for a single datapoint trained with the backpropagation algorithm to calculate derivatives for a gradient descent optimizer. I am primarily looking for ...
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9 votes
3 answers
416 views

This is a follow up of A simple definite integrator class of a single variable in C++. I took most of the advice from Emma X and some from sudo rm -rf slash. Here is my fully revised code: Integrator....
Francis Cugler's user avatar
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2 answers
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I have written a simple Integrator class in C++17 that can perform either a definite single integration of a single variable or a definite double integration of a ...
Francis Cugler's user avatar
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4 votes
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3k views

I am teaching myself some coding, and as my first "big" project I tried implementing a Steepest Descent algorithm to minimize the Rosenbrock function: $$f(x, y) = 100 (y - x^2)^2 + (1 - x)^2$$ The ...
Blue's user avatar
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3 votes
1 answer
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I have made a linear interpolation functions as a side project of mine. It assumes everything is sorted before hand - x and f(x) are the same length. I would like to ask for: general recommendations ...
Stavros Avramidis's user avatar
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3 votes
2 answers
120 views

I have the following code, that defines: A polynomial struct with some useful functions. The newton Raphson algorithm for polynomials. and calculates sqrt(2). What ...
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2 votes
1 answer
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Please see the following code. I am using it to calculate the double integration. Please help me to improve the code. ...
Shankar_Dutt's user avatar
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7 votes
3 answers
6k views

I came up with this recursive pure-Python implementation of De Casteljau's algorithm for computing points on a Bézier curve: ...
das-g's user avatar
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3 votes
4 answers
1k views

I have implemented the Simpson's rule for numerical integration. Check this video for the implemented function. ...
user366312's user avatar
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1 vote
1 answer
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I am interested in doing a 2D numerical integration. Right now I am using the scipy.integrate.dblquad but it is very slow. Please see the code below. My need is to ...
Shankar_Dutt's user avatar
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1 vote
2 answers
653 views

The following is an implementation of Newton's method of finding root of a function. ...
user366312's user avatar
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1 vote
2 answers
398 views

I made this code to compute definite integrals in Processing. It works by getting the rectangle between the maximum value between the previous function value and the current function value, and then I ...
Simple coder's user avatar
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1 answer
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I'm a newbie playing around with Fortran 90 and openmp and wrote the code below (a simple 2D heat transfer simulation) for testing purposes. So far I don't see any speedup by using openmp / parallel ...
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