Algorithms which solve mathematical problems by means of numerical approximation (as opposed to symbolic computation).
2
votes
2answers
60 views
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 ...
4
votes
2answers
59 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 ...
4
votes
0answers
99 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 ...
3
votes
1answer
36 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 ...
4
votes
2answers
57 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
votes
1answer
48 views
Integer square root
This essentially performs the same function as exact-integer-sqrt in math.numeric-tower.
...
3
votes
1answer
38 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 ...
3
votes
1answer
30 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
votes
1answer
57 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
votes
1answer
61 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 ...
3
votes
4answers
133 views
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 (...
6
votes
1answer
118 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 ...
10
votes
3answers
90 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
votes
1answer
109 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 ...
3
votes
1answer
100 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 ...
3
votes
1answer
97 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 ...
3
votes
1answer
135 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 ...
4
votes
1answer
241 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 ...
2
votes
1answer
67 views
Golden Section Search in Lisp
I implemented the golden section search algorithm recursively in Lisp. My code is:
...
3
votes
0answers
58 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 ...
3
votes
3answers
358 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 ...
2
votes
2answers
95 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.
...
2
votes
0answers
25 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 ...
8
votes
4answers
192 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
votes
1answer
99 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
votes
3answers
89 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
votes
1answer
56 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 ...
4
votes
1answer
222 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 ...
1
vote
2answers
121 views
2
votes
0answers
61 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 ...
0
votes
1answer
99 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 ...
5
votes
1answer
249 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:
$$
B(p^2) = C\int_0^{p^2}f_1\left(B(q^2),q^2\right)\mathrm{d}q^2 + C\int_{p^2}^{\Lambda^2} ...
1
vote
2answers
197 views
Bisection method for finding the root of a function
For those who aren't familiar with the bisection method for finding the root of a function (i.e. finding where \$f(x) = 0\$) the basic idea is:
Take a function \$f(x)\$ and an interval \$[a,b]\$
If ...
3
votes
1answer
92 views
Comparing multiple arguments and returns the smallest argument
I want to see if anyone knows how to optimize the code below:
...
4
votes
2answers
1k views
Square Root Calculator
I have now written a simple square root calculator using the division method:
...
3
votes
0answers
58 views
Volatility updating with Heston-Nandi model
I'm trying to program a volatility updating rule using iteration. I start with the well-known Heston-Nandi model where the returns dynamics are:
$$
\left\{
\begin{array}{rcl}
R_{t+1} ...
2
votes
2answers
128 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
votes
2answers
669 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
votes
2answers
109 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
votes
1answer
236 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 ...
14
votes
6answers
7k 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 ...
8
votes
5answers
671 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
votes
2answers
222 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 ...
6
votes
2answers
172 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:
$$p ...
4
votes
2answers
10k views
Trapezoidal rule to approximate the integral of x^2
I've implemented the trapezoidal rule to compute the integral for a function \$x^2\$. I would like to see another style of the same code. It seems Matlab hates for a matrix to be expanded without ...
3
votes
1answer
67 views
How can I make this Euler/RK4 implementation more elegant?
One of the things that I'm doing to teach myself is converting some numerical methods from existing Python code (they seem to me to lend themselves to functional programming quite well).
I'd like to ...
5
votes
1answer
1k views
Fixed point iteration and cobweb plot
I'm using Python to find fixed points of a given function and then draw a cobweb plot to visualize it. Thanks to this question, I have the core of the code written and can accomplish the task, but I ...
10
votes
6answers
2k views
Approximating the square root using an iterative method
I wrote this code, based on the Newton-Raphson method, to find the square root of a number. I'm wondering how I can optimise this code, as I am out of ideas.
...
6
votes
2answers
4k views
Newton's method to solve cubic equations
I have used the Newton-Raphson method to solve Cubic equations of the form $$ax^3+bx^2+cx+d=0$$ by first iteratively finding one solution, and then reducing the polynomial to a quadratic ...
6
votes
1answer
1k 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 ...
