Questions tagged [numerical-methods]

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

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2answers
269 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
770 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 ...
26
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6answers
25k 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
1k 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
432 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
331 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
91 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 ...
44
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8answers
7k views

Prettify math formula in code

I have a function to calculate the normal distribution in Python: ...
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. ...
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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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2answers
2k views

Recursive calculation of second order derivative

I am writing code to do some numerical task using the routines of the book Numerical Recipes. One of my objectives is to calculate the second derivative of a function and have a routine that ...
8
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1answer
4k views

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 ...
11
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2answers
4k views

Sqrt (square root) function

As an exercise in learning Scala, I implemented a square root function like this: ...
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3answers
3k views

Approximating sines and cosines using up to five terms of the Taylor series

I have one programming question: The sine and cosine of \$x\$ can be computed as follows: \$\sin(x) = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \frac{x^9}{9!} - \dots\$ ...
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2answers
2k views

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
2k views

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 ...
4
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1answer
877 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 ...
2
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1answer
1k views

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
2k views

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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