Questions tagged [numerical-methods]

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

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4
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2answers
590 views

Calculating pi by adding areas of thin rectangles

I wrote a small program for fun to try to prove Pi by taking a certain precision and radius and using it to calculate the area of the circle. My method should be giving me an area that is just ...
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2answers
591 views

Visualizing Newton-Raphson method for finding zeroes of a function

I have created a program to visualize the working of Newton-Raphson method to find the zeroes of a function: newton.m: ...
4
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2answers
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Implementation of exp function in C using Taylor Series expansion

I am trying to write code to calcultate ex using: $$e^x = \sum_{n=0}^\infty \frac{x^n}{n!} = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \cdots $$ This is the code I have, which works ...
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3answers
839 views

1D shock tube problem written in Fortran

I have written a simple Euler solver for the 1D shock tube problem. Eventually, I plan to extend this code to solve the full 3D compressible Navier-Stokes equations. Therefore, I want to start with ...
7
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1answer
2k views

Linear Interpolation C++

I have to write a collection of methods for performing linear, bilinear and trilinear interpolation. I have also to write some tests to show that interpolation is exact for polynomials (which should ...
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1answer
143 views

Square root calculation in Scheme (SICP Exercise 1.7)

I have done exercise 1.7 in SICP (calculate square root precision when change in guesses is under a certain value), but I am calling the change-in-precision function twice in each iteration, which ...
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2answers
147 views

`atof` revisited

In an answer to this question I mentioned best effort. Here I try to explain what I meant. Please keep in mind that the implementation is intentionally incomplete (missing features such as ...
2
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1answer
93 views

Integer square root

This essentially performs the same function as exact-integer-sqrt in math.numeric-tower. ...
4
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2answers
152 views

Computing the double Integral using MonteCarlo techniques using Julia

I decided to try and learn Julia for doing scientific computing, and I decided to tackle the problem of finding $$ \int_{D_{\frac{1}{4}}} x^4 + y^2 dA $$ where \$ D_{\frac{1}{4}} \$ is the part of ...
4
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1answer
606 views

Linear shooting method to solve a B.V.P

I have wrote a code to approximate the solution of a boundary value problem: x'' = p(t)x'(t)+q(t)x(t)+r(t) x(b) = beta in [a,b] by using Runge-Kutta method ...
2
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1answer
2k views

Double integral solver in TI-84

Here's a program I made for estimating a double integral over a general region. It's pretty accurate, but it's VERY, VERY slow. (Getting an accurate enough result takes about 30 seconds) Here's the ...
6
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1answer
246 views

Approximating π via Monte Carlo simulation

Inspired by a tweet linked to me by a friend and a Haskell implementation by her for the same problem, I decided to try my hand at approximating the value of π using everything in the Haskell standard ...
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4answers
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Computing integer square roots in Java - follow-up

(See the previous iteration.) My two previous methods for computing the integer square root of a number \$N\$ ran in the \$\mathcal{O}(\sqrt{N})\$ worst case time. Now I have added a method (...
9
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1answer
495 views

Gamma function in Rust

The gamma function is one of a couple nice continuous extensions to the traditional factorial function. I used this Python program as a reference, which in turn, uses this Ada program. As the Ada ...
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3answers
114 views

Reinventing the Math Functions

Just for practice in the mathematical side of programming, I decided to rewrite the math functions, with the addition of the root() function, which the Math library ...
5
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1answer
375 views

Newton's Method Polynomial solver in Ruby

I am learning Ruby programming from "Learn Ruby the Hard way" and I am doing the "Ruby koans". I have heard a little bit about "Idiomatic" Ruby but I don't know much about it. How can I make it more ...
4
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1answer
191 views

Simple neural-network simulation in C++ (Round 4)

You may want to take a look at Rounds 1, 2, and 3, though that isn't necessary for understanding what's below. The major change since Round 3 is that my code is much cleaner and I'm including ...
4
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1answer
221 views

Simple neural-network simulation in C++ (Round 3)

As I mentioned at the end of my Round 2 answer, I've needed to expand my code in order to produce faithfully the data needed for Figure 1 of this paper. Unfortunately, the updates have made my script ...
4
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1answer
215 views

Simple neural-network simulation in C++ (Round 2)

Intro Yesterday I posted this question. Since then, I've updated my code to incorporate these suggestions. I've also removed the dependence on C++11. Finally, I've made the following changes that ...
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1answer
2k views

Simple neural-network simulation in C++

The C++ code below simulates the timecourse of the membrane potential (V) of a population of 128 leaky integrate-and-fire ...
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1answer
92 views

Golden Section Search in Lisp

I implemented the golden section search algorithm recursively in Lisp. My code is: ...
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0answers
64 views

Decorator for setting up bracketing rootfinding functions

I'm looking for comments on the use of decorators for the following problem (validating initial guesses for bracketing rootfinding methods), as well as any other comments you might have on the design ...
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3answers
6k views

Implementation of Brent's Algorithm to find roots of a polynomial

I made a program that contains a root-finding algorithm for polynomials as a function and contains 3 test polynomials. The algorithm is Brent's method and is based entirely off the pseudocode from ...
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2answers
1k views

Root-finding by iterated bisection

Both of the following code give the same result. But I'm not sure where should I put the raise statement. ...
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0answers
31 views

Iterative procedure to get 3D coordinates from distance constraints

Imagine you have a series of n points randomly generated in a box in 3D space. You also have a list of distance bounds, e.g. points 5 and 3 should be between 1.0 and 2.0 Angstroms apart. There are ...
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4answers
1k views

Buffon's Needle experiment

I was working on a program that simulates the Buffon's Needle experiment. If anyone is not familiar with it, a Wiki link is provided - Buffons's Needle The point of Buffon's experiment is to find ...
7
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1answer
194 views

Monte Carlo Pi (MASM)

I'm currently trying to brush up on my assembly skills and, being at the FPU section of the tutorial, I implemented a very basic version of a Monte-Carlo-Algorithm to compute pi. I deliberately use ...
2
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3answers
97 views

Calculating e^x by math.h and by own means

For this program, the user needs to enter an exponent and the program will calculate \$e\$ (Euler's number) to the power of the exponent the user inputs. This is done by two ways: By the math.h ...
2
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1answer
419 views

Utility Method to find the Square root of a number

Utility to calculate the square root of a number. The method also accept an epsilon value, which controls the precision. The epsilon value could range to any number including zero. I am expecting a ...
5
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1answer
1k views

Poker Odds Calculation with Monte Carlo

I have created an Odds Calculator in Java. The program gives me the odds, but I want to make sure that they are correct. Maybe someone can tell me a calculator I can compare my results with or knows ...
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2answers
557 views

Functional abstraction to find nth root of a number - Newton raphson

Below is the solution: ...
5
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1answer
378 views

Terry Feagin's 10th order explicit Runge-Kutta method

The following Julia code implements Terry Feagin's 10th order explicit Runge-Kutta method (a more accurate cousin of RK4). Though the structure of the code is quite simple (i.e. no cyclomatic ...
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1answer
117 views

Summation for π [closed]

I was going through my Java book's exercise solutions and comparing and incorporating the author's techniques into my repertoire. Most of the time, my approach is identical to the author's. When it ...
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1answer
2k views

Iterative equation solver in Python

In order to solve a equation where the left hand side appears under an integral on the right hand side: $$ B(p^2) = C\int_0^{p^2}f_1\left(B(q^2),q^2\right)\mathrm{d}q^2 + C\int_{p^2}^{\Lambda^2} f_2\...
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2answers
667 views

Bisection method for finding the root of a function

For those who aren't familiar with the bisection method for finding the root of a function (i.e. finding where \$f(x) = 0\$) the basic idea is: Take a function \$f(x)\$ and an interval \$[a,b]\$ If \$...
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1answer
406 views

Comparing multiple arguments and returns the smallest argument

I want to see if anyone knows how to optimize the code below: ...
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2answers
4k views

Square Root Calculator

I have now written a simple square root calculator using the division method: ...
3
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0answers
106 views

Volatility updating with Heston-Nandi model

I'm trying to program a volatility updating rule using iteration. I start with the well-known Heston-Nandi model where the returns dynamics are: $$ \left\{ \begin{array}{rcl} R_{t+1} &=&...
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2answers
2k views

Newton's square root

This is the code I wrote to compute the newton's square root of a number. I aimed for extreme clarity over efficiency and I have put an abundant docstring at the start of the ...
14
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2answers
3k views

Pi by Monte-Carlo

I was inspired by this SO post to investigate a good Java8 way to calculate Pi based on simulation. I used a similar task to learn about parallel programming on both CUDA, and Intel Xeon Phi ...
3
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2answers
249 views

Multifunctional Monty Hall Simulator

Based on this question on math.SE regarding probabilities in variations on the Monty Hall problem, I cobbled up a simulator in Ruby to give myself an introduction to the language. Since this is my ...
3
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1answer
699 views

Percentage based drop prize on Mob entity kill

I have created a simple percentage-based random prize drop for killing certain mobs. A drop is basically what the player will get in return for killing a mob, as a reward. So I have a large list of ...
25
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6answers
24k views

Monte Carlo pi calculation

In order to learn the basics of Monte Carlo I calculated pi with it. I also wrote an explanation of the reasoning behind the code. Down here you can see the circle with random points that I simulated ...
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5answers
959 views

Probabilistic matchmaking simulation

The following is a problem I found on this wiki. What can I do to optimize my algorithm, and make this code more C++11? Write a program to discover the answer to this puzzle:"Let's say men and ...
3
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2answers
418 views

Hamiltonian Monte Carlo in Scala

I'm writing a program in Scala to perform Hamiltonian Monte Carlo (HMC), coupled with Gibbs sampling of some variables. The algorithm, with the modifications such as perturbing epsilon and l and ...
7
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2answers
327 views

Monte Carlo estimation of the Hypergeometric Function

I am trying to implement the algorithm described in the paper Statistical Test for the Comparison of Samples from Mutational Spectra (Adams & Skopek, 1986) DOI: 10.1016/0022-2836(87)90669-3: $$p =...
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2answers
26k views

Trapezoidal rule to approximate the integral of x^2

I've implemented the trapezoidal rule to compute the integral for a function \$x^2\$. I would like to see another style of the same code. It seems Matlab hates for a matrix to be expanded without ...
4
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1answer
90 views

How can I make this Euler/RK4 implementation more elegant?

One of the things that I'm doing to teach myself is converting some numerical methods from existing Python code (they seem to me to lend themselves to functional programming quite well). I'd like to ...
5
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1answer
4k views

Fixed point iteration and cobweb plot

I'm using Python to find fixed points of a given function and then draw a cobweb plot to visualize it. Thanks to this question, I have the core of the code written and can accomplish the task, but I ...
11
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6answers
4k views

Approximating the square root using an iterative method

I wrote this code, based on the Newton-Raphson method, to find the square root of a number. I'm wondering how I can optimise this code, as I am out of ideas. ...