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Questions tagged [numerical-methods]

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

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1answer
41 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 ...
4
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1answer
83 views

C++ Pi Calculator - Leibniz Formula

Hi :) 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 ...
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2answers
1k views

Calculate Pi using Monte Carlo

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1answer
34 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, ...
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1answer
50 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: ...
12
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2answers
490 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
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1answer
91 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
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3answers
106 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
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1answer
66 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 ...
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0answers
38 views

Solving heat equation using forward finite differences [closed]

I am trying to improve a procedure that uses explicit forward finite differences for solving the heat equation. It is typically the scheme shown below. (32-bit program Delphi XE10.1) ...
4
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0answers
49 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 ...
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0answers
72 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 ...
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0answers
122 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 ...
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0answers
77 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
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3answers
353 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
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3answers
739 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 ...
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1answer
133 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
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1answer
155 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
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2answers
87 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
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3answers
1k 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
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0answers
128 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
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1answer
71 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
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2answers
3k 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 ...
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0answers
214 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 ...
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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. ...
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1answer
74 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
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1answer
229 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\$: ...
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3answers
2k 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: ...
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0answers
243 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 ...
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0answers
828 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 ...
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0answers
194 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
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3answers
418 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
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1answer
189 views

Computing the improper integral of several functions

How can I optimize and make prettier the following code? Main.cpp ...
3
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3answers
68 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
149 views

Spectrum Analysis with Discrete Fourier Transform

Here is a simple implementation of the Discrete Fourier Transform: myFourierTransform.m ...
5
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3answers
3k 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 ...
4
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1answer
404 views

Hodgkin-Huxley model in C++

I'm fairly new to C++ and I want to simulate the Hodgkin-Huxley neuron model with it. I have used a MATLAB implementation before and I hope that the C++ code will be faster. Both seem to take the ...
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2answers
355 views

Bisection method solver

I have a simple bisection method solver that I was told it has some problems in design and I need my code to be reviewed, so I was hoping for someone to give me guideline on how to improve my code. ...
2
votes
0answers
331 views

Computing the square root of a number using binary search

This is implemented in MIPS assembly. I've hard-coded the initial guess, as I haven't figured out how to allow the user to input a negative or non-negative integer to then display the result back to ...
4
votes
2answers
530 views

Discrete random number generator in Python

Description: I am given a list of possible values, each of which have an associated probability of occurrence. How could I improve the algorithm that randomly generates a value based on the given ...
5
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2answers
267 views

Python numerical integration

Could the time complexity of this definite integral algorithm be improved? ...
3
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1answer
73 views

Area under curve and its volume as solid of revolution

I would like to know if there is some more "elegant" way to write these 3 functions. Any tip or idea is welcome. ...
6
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1answer
294 views

Calculating pi to 7 significant figures without using Math.PI

I need to calculate pi to 7 significant figures in Java—without using Math.PI. Here is the code I came up with to do that: ...
3
votes
1answer
276 views

Monte Carlo Simulation of P-Value

I'm testing Python 3 code to perform a Monte Carlo simulation based on the result of an statistical test. I currently have the result of the statistical test in a pandas dataframe, like this. ...
5
votes
1answer
701 views

AVX assembly for fast atan2 approximation

I'm writing a fast atan2 approximation, and would like some feedback on my assembly in particular. I know one of the first things is that people will question why I'm using inline assembly instead of ...
3
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2answers
211 views

SICP - exercise 1.7 better end test for square root approximation

Here is exercise 1.7 from SICP: Exercise 1.7 The good-enough? test used in computing square roots will not be very effective for finding the square roots ...
5
votes
2answers
760 views

Runge-Kutta fourth order integration

I have written a simple code for Runge-Kutta fourth order integration to solve a system of ordinary differential equations and parallelized it using OpenMP. I don't know if it is the best we can do ...
6
votes
1answer
2k views

Monte Carlo simulation to approximate the value of PI

This is a C++ implementation of a simple Monte Carlo simulation to approximate the value of pi. The program uses the standard library Mersenne twister engine to generate two random numbers between -1....
12
votes
1answer
170 views

Calculate the closest point to many hyperbolic paraboloids

In this question I asked for a way to compute the closest projected point to a hyperbolic paraboloid using python. Using the iterative approximation answer, I'm able to use the code below to ...
3
votes
1answer
128 views

Area under curve

The following code is a solution to a Hackerrank problem in Haskell. Given a list of polynomial coeficients a and exponents b, ...