Questions tagged [numerical-methods]

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

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1answer
453 views

C++ HyperLogLog Implementation

I'm a scientific C programmer moving my way over to using Modern C++. I found myself needing a HyperLogLog implementation, and I wanted to use this for practice. I plan to move a number of these ...
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0answers
104 views

Computing nth roots of a number - SICP exercise 1.45

From SICP Exercise 1.45: We saw in 1.3.3 that attempting to compute square roots by naively finding a fixed point of x/y does not converge, and that this can be fixed by average damping. ...
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1answer
170 views

Approximating pi/4 using Wallis Product - SICP exercise 1.31

From SICP The sum procedure is only the simplest of a vast number of similar abstractions that can be captured as higher-order procedures. Write an analagous procedure called product that ...
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1answer
1k views

Computing exponential function by Taylor Series without overflow

The original question is to write a Fortran program to compute the sum of the first 20 terms in the exponential equation (for x=1,2,3,4,5): $$\sum_{n=0}^\infty \frac{x^n}{n!} = 1 + \frac{x^1}{1!} + \...
3
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2answers
160 views

Calculating Pi with Android

I'm kind of new to Java but I am writing an Android app. Right now I'm working on an async task to calculate Pi but when I run it the memory usage increases alarmingly (+5MB per second). This one ...
2
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1answer
64 views

Evaluation of e^x with series expansion

My code calculates \$e^x\$ with series expansion. Is there any way to make it shorter and cleaner? ...
6
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2answers
541 views

Monte-Carlo method to estimate Pi runs slower in multiple threads, than in single thread

I'm learning Scala, and I wrote a program to estimate the value of Pi. When I'm using multiple threads, it takes 5-6 times longer to calculate the same iterations. I wrote a similar program in Java, ...
5
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1answer
389 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 ...
2
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1answer
277 views

Calculation of elasticity for non-linear curve

I've written this code to calculate the elasticity for econometric analysis. Basically, this algorithm estimate the function: $$\epsilon(x) = \frac{x}{f(x)}\ f'(x)$$ ...
5
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1answer
371 views

Generate dictionary of points on n-sphere

This is a long-shot, but my question is to simply optimize this particular function in some code I have written: ...
5
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1answer
2k views

Evaluating a series of Legendre polynomials

The following function represents the electrostatic potential, in spherical coordinates, due to a ring of charge \$q=1\$ and radius \$R=1\$, placed in the plane \$x\$-\$y\$: $$\phi(r,\theta) = \sum_{...
8
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3answers
862 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
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1answer
2k views

Calculate the arclength

I am trying to estimate a good approximation for the arclength of the curve \$ y = \sqrt{1-x^2}\$ for \$x \in [0, 1]\$. I did this using a Bezièr curve, and made it so that the area under the two ...
4
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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 ...
5
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2answers
423 views

Monte Carlo simulation of amoeba population

I wrote a simple Python simulation to answer the "Amoeba" population question posed here: A population of amoebas starts with 1. After 1 period that amoeba can divide into 1, 2, 3, or 0 (it can die)...
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0answers
68 views

Numerical differentiation using the y-intercept

I have a routine for determining the derivative of a function using the y-intercept (B) to infer the finite difference step (h). ...
4
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2answers
599 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 ...
4
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2answers
3k 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 ...
3
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1answer
153 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
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2answers
154 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 ...
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1answer
94 views

Integer square root

This essentially performs the same function as exact-integer-sqrt in math.numeric-tower. ...
4
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1answer
617 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
253 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 (...
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1answer
508 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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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
116 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 ...
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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 ...
4
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1answer
231 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 ...
5
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1answer
380 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
195 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 ...
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2answers
328 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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1answer
92 views

Golden Section Search in Lisp

I implemented the golden section search algorithm recursively in Lisp. My code is: ...
5
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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 ...
7
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1answer
195 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 ...
3
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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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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
32 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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2answers
672 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 \$...
8
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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 ...
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 ...
3
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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 ...
6
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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\...
2
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1answer
422 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 ...
0
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1answer
118 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 ...
3
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1answer
424 views

Comparing multiple arguments and returns the smallest argument

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

Square Root Calculator

I have now written a simple square root calculator using the division method: ...