Questions tagged [numerical-methods]
Algorithms which solve mathematical problems by means of numerical approximation (as opposed to symbolic computation).
167
questions
21
votes
4answers
2k views
IEEE 754 square root with Newton-Raphson
I have an implementation of the sqrt function that uses a combination of IEEE 754, packed bitfields, and the Newton-Raphson algorithm:
...
13
votes
2answers
975 views
Mean π: Archimedes vs. Gauss - π computation through generalized means
I've written this simplified code to compute Pi for educational/demonstration purposes.
These methods are based upon the generalized means: see a presentation on Pi and the AGM.
Archimedes' method ...
2
votes
1answer
57 views
Arbitrary precision Euler-Mascheroni constant via a Brent-McMillan algorithm with no math module
Utilizing the below relation, I am able to compute the Euler constant to great precision on a single thread quickly and simply.
My process is to compute the natural log via the AGM(utilizing Pi an ...
1
vote
1answer
41 views
Euler-Mascheroni Single Thread Speed Improvements
The below code was written to generate γ, for educational purposes.
My general methodology is as follows:
Compute Gamma via the accepted answer's algorithm here.
In order to do this I need to ...
4
votes
1answer
64 views
Calculate the Euler-Mascheroni constant without the math module
The below code was written to generate γ, for educational purposes.
Single threaded, no functional zeroes required, no binary splitting(which can all be used to compute competitively like y-cruncher, ...
12
votes
3answers
4k views
Python π = 1 + (1/2) + (1/3) + (1/4) - (1/5) + (1/6) + (1/7) + (1/8) + (1/9) - (1/10) …1748 Euler
I wrote this code to show that my reddit post is correct.
After the first two terms, the signs are determined as follows: If the denominator is a prime of the form 4m − 1, the sign is positive; if ...
2
votes
1answer
62 views
Trapezoidal rule for set of data
Here is the question from the book of Mark Newman-Computational Physics Exc 5.1
a) Read in the data and, using the trapezoidal rule, calculate from them the approximate distance traveled by the ...
4
votes
1answer
51 views
Evaluating π using Monte Carlo methods - Serial vs OMP
I wrote this simple code for evaluating the π using Monte Carlo method. This is the serial version:
...
11
votes
0answers
55 views
Continuous Fourier integrals by Ooura's method
I have a PR implementing Ooura and Mori's method for continuous Fourier integrals. I used it here to compute an oscillatory integral that Mathematica got completely wrong, and then I thought "well ...
7
votes
1answer
129 views
Parallel Ramanujan's formula for 1/π calculation
I finished my university project for calculating \$1/\pi\$ and I would love to get some feedback.
Before you guys jump into this code please keep in mind newcomer to C++ just decided to use it for ...
6
votes
0answers
68 views
Numerical integration in cython
I have a set of nested functions that I need to call multiple times. I know scipy.quad is pretty fast, but I will need to call the integrator recursively and want ...
7
votes
2answers
139 views
Simple function that simulates survey results based on sample size and probability
What is this:
This is a simple function, part of a basic Monte Carlo simulation. It takes sample size and probability as parameters. It returns the simulation result (positive answers) plus the input ...
3
votes
1answer
84 views
Calculating pi via collisions
This code calculates pi via collisions; it asks for a user input of N which determines the mass of the second block. It is fully working, it just takes forever to run when N >= 2. I want to be able ...
3
votes
1answer
46 views
Monte Carlo pi animation
I have created a program that calculates pi using a Monte Carlo method. It also animates the process and displays the value as it is updated to show how it gets closer and closer to the actual value ...
6
votes
1answer
70 views
Monte Carlo errors estimation routine
I would value your opinion on the following piece of code. I am rather new to both Python and Monte Carlo analysis, so I was wondering whether the routine makes sense to more experienced and ...
2
votes
1answer
101 views
Java Pi Calculation using an Averaged-Leibniz formula
While trying to discover a way to calculate the digits of Pi faster with the Leibniz formula for Pi, I noticed that, if I took two consecuent numbers in the series, and calculate their average, I ...
6
votes
1answer
506 views
C++ Pi Calculator - Leibniz Formula
Yesterday I saw a CodeTrain video in where Daniel Shiffman tried to approximate Pi using the Leibniz series. It was interesting so I decided to try it too.
I wrote this console application with a ...
11
votes
2answers
2k views
0
votes
1answer
41 views
A simple clusterness measure of data in one dimension using Java
Problem definition
Given \$X = (x_1, \dots, x_n)\$ such that \$x_1 \leq x_2 \leq \dots \leq x_n \$. Let \$x_{\min} = \min X = x_1\$, \$x_{\max} = \max X = x_n\$ and \$r = x_{\max} - x_{\min}\$. Also, ...
3
votes
1answer
78 views
Polynomial implementation in Golang
I am writing a numerical analysis library in golang for which I need to implement a polynomial struct. Here is the source code:
...
13
votes
2answers
1k views
Simulating a two-body collision problem to find digits of Pi
I came across a nice video on 3Blue1Brown's channel that highlights a very indirect way to find the digits in Pi. I'd suggest watching the whole video, but briefly:
The setup is as above. A "small" ...
9
votes
1answer
123 views
Discrete Lanczos Derivatives
I have a PR implementing denoising discrete Lanczos derivatives, following this paper. The following code works well, but the design is a train wreck, and I was hoping to get some advice to improve it....
3
votes
3answers
109 views
A collection of vector functionals
I would like some feedback for a collection of what I call "vector functionals", by which I mean maps \$\ell\colon \mathbb{K}^{n} \to \mathbb{K}\$, where the field \$\mathbb{K} = \mathbb{R}\$ or \$\...
4
votes
1answer
92 views
Complex Newton's Method
I'm trying to build a complex Newton's method. I've submitted a PR here, where you can see the documentation and tests, as well as get a compiling example. I'd appreciate y'alls help reducing the ...
4
votes
0answers
69 views
Bisection and Newton's method for finding a root of an equation
In an attempt to learn Rust, I've written up implementations of the bisection method and Newton's method for finding roots of an equation. Both methods come in two variants: the first one searches for ...
7
votes
0answers
100 views
Metropolis Monte Carlo Sampler in Rust
the following is an implementation of the standard Metropolis Hastings Monte Carlo sampler. You can read more about it here.
At the end I am going to give you a link to the Rust playground, so you ...
5
votes
1answer
239 views
Verilog implementation of trapezoidal integration method
Any and all comments are welcome in this review.
Problem
I've been doing a lot with numerical integration methods recently and have mostly been programming in Python. But...speedups! And FPGAs are ...
7
votes
1answer
101 views
Implementing numerical integration in Python
I have this Python code that implements a rectangular numerical integration. It evaluates the (K-1)-dimensional integral for arbitrary integer \$K \geq 1\$
$$\int_{u_K = 0}^{\gamma}\int_{u_{K-1} = 0}^...
7
votes
3answers
900 views
Implementing numerical integration
I have this C++ code that implements a rectangular numerical integration. It evaluates the \$K\$-dimensional integral
$$\int_{u_K = 0}^{\gamma}\int_{u_{K-1} = 0}^{\gamma-u_K}\cdots\int_{u_2}^{\...
5
votes
3answers
946 views
Bisection to find roots in C++
I have written a short C/C++ code finding root by bisection. (This is a simple iterative numerical method allowing to find the root of an equation i.e. x such that f(x) = 0). Bisection Method
The ...
7
votes
1answer
268 views
2d linear Partial Differential Equation Solver using finite differences
This is code that solves partial differential equations on a rectangular domain using partial differences. fd_solve takes an equation, a partially filled in output, ...
5
votes
1answer
182 views
Compute PI in Kotlin on a T-shirt
I have written code in Kotlin with the objective of computing Pi in few enough lines so that it looks good on a t-shirt.
Can be cut and paste into http://try.kotlinlang.org under "My Programs" and ...
5
votes
2answers
91 views
Calculating Maclaurin series for sin(x)
I'm very new to Haskell as was hoping to get some feedback on my code AND I have some specific questions. I've posted code below or you can see it here.
I'd welcome ideas on how better to calculate ...
12
votes
3answers
2k views
Definite Integral Approximation using the Trapezoidal Method
I wrote a program to calculate the value of Definite Integral of a function from a to b. It used the trapezoidal approximation ...
4
votes
0answers
211 views
Numerical integration with Numba
I'm a bit new to working with Numba, but I got the gist of it. I wonder if there any more advanced tricks to make four nested for loops even faster that what I have ...
3
votes
1answer
78 views
A single function for implementing Newton forward and backward polynomial interpolation
On various websites, I've come across a lot of realizations of Newton polynomial interpolation that use separate functions for forward and backward interpolation, respectively. Such solutions seem ...
5
votes
2answers
5k views
Compute a numerical derivative
Since I could not get numpy.gradient() to compute a derivative successfully, I wrote a script to compute it manually. Running the script below will output a plot of ...
3
votes
0answers
399 views
Complex multiplication and integration with CUDA
I want to perform multiplication on two vectors and integrate it in a vector called acc_y. The acc_y variable will update over ...
19
votes
9answers
4k views
Approximating constant π² to within error
This function takes as input float error and approximates constant π² to within error by computing this sum, term by term, until the difference between the new and the previous sum is less than error. ...
1
vote
1answer
76 views
Runge-Kutta Fourth Order in C
I've found that the Runge-Kutta (4th order) calculations in some software I wrote are the bottleneck. Is there anything obvious I can do to improve efficiency here?
Note that Compiler optimizations ...
4
votes
1answer
292 views
Computing an approximate value of Pi via Monte Carlo method in Java with streams
I have this short program that attempts to compute an approximate value of \$\pi\$:
...
5
votes
3answers
3k views
Numeric double integration
I've made a simple program for numerically aproximating double integral, which accepts that the bounds of the inner integral are functions:
...
5
votes
0answers
401 views
Quasi-Random Number Generators
I would like to communicate a piece of code which I hope will soon be broadly useful for everyone who programs in C++: A set of quasi-random number generators proposed for addition to boost.random. To ...
3
votes
0answers
1k views
Numerical Differentiation by Finite Differences
Numerical differentiation is known to be ill-conditioned unless using a Chebyshev series, but this requires global information about the function and a priori knowledge of a compact domain on which ...
1
vote
0answers
206 views
Numerical differentiation on sphere with Python
I have ported from Fortran to Python an algorithm that calculates the numerical derivative along the x direction (longitudinal) of a scalar function s on a ...
8
votes
3answers
526 views
Multithreaded Monte-Carlo Integration
I have a PR implementing multithreaded naive Monte-Carlo integration here. My requirements for the class are the following:
It should support progress reporting, ETA, and graceful cancellation.
It ...
6
votes
1answer
222 views
Computing the improper integral of several functions
How can I optimize and make prettier the following code?
Main.cpp
...
3
votes
3answers
74 views
Newton's algorithm for a polynomial of arbitary degree
Improvement over the last one I posted (now deleted, had no answers and was only cubics). Uses Horner's algorithm this time...
...
3
votes
2answers
255 views
Spectrum Analysis with Discrete Fourier Transform
Here is a simple implementation of the Discrete Fourier Transform:
myFourierTransform.m
...
8
votes
3answers
5k views
Finding the root of a function by Bisection Method
The program has to look for a root in an interval [a,b]. The root should be declared with a certain accuracy eps. I.e it should ...
