Questions tagged [numerical-methods]

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

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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
201 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 ...
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0answers
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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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2answers
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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
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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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2answers
705 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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4answers
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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 ...
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3answers
100 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 ...
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1answer
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Solving an ODE numerically with forward Euler method

The goal is to solve an ODE numerically with forward Euler method. The programs works well (numerical solution really near analytical one). The problem I see is that the Euler scheme don't jump to ...
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1answer
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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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1answer
434 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 ...
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1answer
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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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1answer
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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 is ...
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1answer
451 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
5k views

Square Root Calculator

I have now written a simple square root calculator using the division method: ...
4
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1answer
892 views

Gees - GPL Euler equation solver

As a little helper I recently had to write a code that solves the 1-D Euler equations. As it serves my purpose well I though others could make use of it as well. The homepage of the code can be found ...
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0answers
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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
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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 ...
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2answers
281 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 ...
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1answer
781 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 ...
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2answers
8k views

Newton's method to solve cubic equations

I have used the Newton-Raphson method to solve Cubic equations of the form $$ax^3+bx^2+cx+d=0$$ by first iteratively finding one solution, and then reducing the polynomial to a quadratic $$a1*x^2+b1*x+...
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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 ...
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2answers
438 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 ...
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1answer
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Integral using Simpson's Rule

As an answer to this problem: Exercise 1.29 Simpson's Rule is a more accurate method of numerical integration than the method illustrated above. Using Simpson's Rule, the integral of a ...
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2answers
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Use Newton's Method to compute sqrt(x)

Given the following task: Use Newton's method to compute the square root of a number. Newton's method involves successive approximation. You start with a guess, and then continue averaging ...
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1answer
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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 ...
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6answers
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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. ...
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2answers
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Square root approximations, implemented two ways

Which version is more efficient in calculating the square root ? There are 2 versions I have written to calculate square root programatically. Note reqs strictly state not using library functions ? ...
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1answer
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Python class that implements the Newton method

Here is a python function I wrote to implement the Newton method for optimization for the case where you are trying to optimize a function that takes a vector input and gives a scalar output. I use ...
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1answer
92 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 ...
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2answers
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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 ...

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