Questions tagged [numerical-methods]

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

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3
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0answers
518 views

Complex multiplication and integration with CUDA

I want to perform multiplication on two vectors and integrate it in a vector called acc_y. The acc_y variable will update over ...
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9answers
4k views

Approximating constant π² to within error

This function takes as input float error and approximates constant π² to within error by computing this sum, term by term, until the difference between the new and the previous sum is less than error. ...
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1answer
79 views

Runge-Kutta Fourth Order in C

I've found that the Runge-Kutta (4th order) calculations in some software I wrote are the bottleneck. Is there anything obvious I can do to improve efficiency here? Note that Compiler optimizations ...
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1answer
398 views

Computing an approximate value of Pi via Monte Carlo method in Java with streams

I have this short program that attempts to compute an approximate value of \$\pi\$: ...
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3answers
4k views

Numeric double integration

I've made a simple program for numerically aproximating double integral, which accepts that the bounds of the inner integral are functions: ...
5
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0answers
500 views

Quasi-Random Number Generators

I would like to communicate a piece of code which I hope will soon be broadly useful for everyone who programs in C++: A set of quasi-random number generators proposed for addition to boost.random. To ...
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0answers
2k views

Numerical Differentiation by Finite Differences

Numerical differentiation is known to be ill-conditioned unless using a Chebyshev series, but this requires global information about the function and a priori knowledge of a compact domain on which ...
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0answers
213 views

Numerical differentiation on sphere with Python

I have ported from Fortran to Python an algorithm that calculates the numerical derivative along the x direction (longitudinal) of a scalar function s on a ...
9
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3answers
603 views

Multithreaded Monte-Carlo Integration

I have a PR implementing multithreaded naive Monte-Carlo integration here. My requirements for the class are the following: It should support progress reporting, ETA, and graceful cancellation. It ...
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1answer
252 views

Computing the improper integral of several functions

How can I optimize and make prettier the following code? Main.cpp ...
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3answers
78 views

Newton's algorithm for a polynomial of arbitary degree

Improvement over the last one I posted (now deleted, had no answers and was only cubics). Uses Horner's algorithm this time... ...
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2answers
353 views

Spectrum Analysis with Discrete Fourier Transform

Here is a simple implementation of the Discrete Fourier Transform: myFourierTransform.m ...
8
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3answers
6k views

Finding the root of a function by Bisection Method

The program has to look for a root in an interval [a,b]. The root should be declared with a certain accuracy eps. I.e it should ...
4
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1answer
574 views

Hodgkin-Huxley model in C++

I'm fairly new to C++ and I want to simulate the Hodgkin-Huxley neuron model with it. I have used a MATLAB implementation before and I hope that the C++ code will be faster. Both seem to take the ...
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2answers
647 views

Bisection method solver

I have a simple bisection method solver that I was told it has some problems in design and I need my code to be reviewed, so I was hoping for someone to give me guideline on how to improve my code. ...
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0answers
487 views

Computing the square root of a number using binary search

This is implemented in MIPS assembly. I've hard-coded the initial guess, as I haven't figured out how to allow the user to input a negative or non-negative integer to then display the result back to ...
4
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2answers
660 views

Discrete random number generator in Python

Description: I am given a list of possible values, each of which have an associated probability of occurrence. How could I improve the algorithm that randomly generates a value based on the given ...
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2answers
350 views

Python numerical integration

Could the time complexity of this definite integral algorithm be improved? ...
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1answer
73 views

Area under curve and its volume as solid of revolution

I would like to know if there is some more "elegant" way to write these 3 functions. Any tip or idea is welcome. ...
6
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1answer
398 views

Calculating pi to 7 significant figures without using Math.PI

I need to calculate pi to 7 significant figures in Java—without using Math.PI. Here is the code I came up with to do that: ...
3
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1answer
439 views

Monte Carlo Simulation of P-Value

I'm testing Python 3 code to perform a Monte Carlo simulation based on the result of an statistical test. I currently have the result of the statistical test in a pandas dataframe, like this. ...
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1answer
1k views

AVX assembly for fast atan2 approximation

I'm writing a fast atan2 approximation, and would like some feedback on my assembly in particular. I know one of the first things is that people will question why I'm using inline assembly instead of ...
3
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2answers
344 views

SICP - exercise 1.7 better end test for square root approximation

Here is exercise 1.7 from SICP: Exercise 1.7 The good-enough? test used in computing square roots will not be very effective for finding the square roots ...
5
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2answers
1k views

Runge-Kutta fourth order integration

I have written a simple code for Runge-Kutta fourth order integration to solve a system of ordinary differential equations and parallelized it using OpenMP. I don't know if it is the best we can do ...
6
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1answer
3k views

Monte Carlo simulation to approximate the value of PI

This is a C++ implementation of a simple Monte Carlo simulation to approximate the value of pi. The program uses the standard library Mersenne twister engine to generate two random numbers between -1....
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1answer
217 views

Calculate the closest point to many hyperbolic paraboloids

In this question I asked for a way to compute the closest projected point to a hyperbolic paraboloid using python. Using the iterative approximation answer, I'm able to use the code below to ...
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1answer
165 views

Area under curve

The following code is a solution to a Hackerrank problem in Haskell. Given a list of polynomial coeficients a and exponents b, ...
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2answers
705 views

Runge Kutta ODE Solver

An ordinary differential equation (ODE) is an equation of the kind $$u'(x)=f(t,u(x)).$$ My program attempts to solve such ODE's numerically through explicit Runge Kutta methods. Instead of writing a ...
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1answer
5k views

ODE45 solver implementation in Python

I have a project where I need ODE solver without dependencies to libraries like Scipy. I decide to implement ODE45. According to tutorials from internet and from what I remember from classes I ...
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0answers
98 views

Scala Functional Programming ODE Solver

I'm new to both Scala and Functional programming. I've been doing the excellent course Functional Programming Principles in Scala on Coursera and I want to test out what I've learned. I've written a ...
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1answer
57 views

Integral implemented using a trapezoidal Riemann sum

I tried to make this a general purpose integral function but I want to know if it's efficient and idiomatic Rust. ...
2
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2answers
77 views

Approximation of error-function erf(x)

The code beyond approximates the error-function erf(x) with following formular \$erf(x)=1-(a_1t+a_2t^2+a_3t^3)e^{-x^2})\$ for \$x\geq0\$ inclusive the identity \$...
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1answer
129 views

Approximating Pi with Polygons

I wrote a program that approximates Pi by using polygons. I used the formulars in the picture beyond. In my code they are called innerPoly (\$c_{2n}\$) and ...
5
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4answers
1k views

Monte Carlo estimation of π

My C program uses the Monte Carlo method to approximate the mathematical constant π, the ratio of a circle's circumference to its diameter (and, importantly for this code, 4 times the ratio of a ...
8
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1answer
176 views

Root finding and integration [closed]

I am trying to implement the modified Next Reaction Method with time varying propensities as mentioned in sections IV and V of this paper. At one step in the process this expression must be evaluated: ...
8
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1answer
959 views

Fitting multiple piecewise functions to data and return functions and derivatives as Fortran code

Background For a future workshop I'll have to fit arbitrary functions (independent variable is height z) to data from multiple sources (output of different ...
2
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0answers
196 views

Estimate π using an infinite series

Looking for style and speed review π PI An estimate is \$\frac{4}{1} - \frac{4}{3} + \frac{4}{5} - \frac{4}{7} + \frac{4}{9} - \frac{4}{11} + \frac{4}{13} - \frac{4}{15} + \frac{4}{17} \$... The ...
32
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8answers
9k views

PI Calculator, Interview Challenge

Greg Beech says here that he asks C# candidates to produce a formula that calculates PI Given that Pi can be estimated using the function \$4 * (1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \dots)\$. ...
6
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1answer
390 views

Double exponential quadrature

I'm trying to lighten the code review load for the maintainers of boost.math, and I was hoping you guys could help me out. I have a pull request which implements tanh-sinh quadrature, which is ...
3
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0answers
139 views

Simple finite difference employing Maccormack technique

I am relatively new to programming and while I am fairly comfortable with the math, I cannot say with confidence that I feel the same way with programming. Anyway here is a simple finite difference ...
7
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1answer
146 views

Computing max t such that tanh(pi*sinh(t)/2) <1

I'm looking for a way to quickly determine that maximum value of t such that tanh(pi/2 sinh(t)) is strictly less than 1, for a ...
6
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2answers
834 views

Implementation of alternating direction implicit method

I have written a program that implements the ADI method and Crank-Nicolson method for solving Schrodinger equations. The program is working, but it takes a very long time to run. I am looking for ...
2
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1answer
533 views

Estimating Pi with random darts on dartboard - high complexity issues

I've been trying to write nice snippet of code to simulate pi estimation by randomly throwing darts on a dartboard. While running the following code on high but reasonable numbers my mac doesn't plot. ...
10
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1answer
1k views

Generate iCalendar .ics files with events for astrological aspects

I'm relatively new to Python, coming from a deep C++ background. I'm mostly looking for feedback on how to make my code more idiomatic/pythonic, but I would welcome and appreciate any and all other ...
2
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1answer
4k views

Polynomial curve-fitting over a large 3D data set

I have a list of 4 images, called listfile.list, which looks like this: image1 image2 image3 image4 Each image has 10 frames containing a 2000 x 2000 array of ...
5
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2answers
375 views

Runge-Kutta 4th order using Python numexpr.evaluate()

I am implementing an ODE solver, where the user provides rates and coefficients as a string. ODE solver has to work with vectors. The best implementation I got so far is the following: ...
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1answer
84 views

A quartic polynomial in four variables, for numerical integration

About half year ago, I derived a integral of a piecewise polynomial, which was a complex formula. Below is one of that formula: Obviously, the above formula has relationship with four varibles \$u_i,\...
2
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1answer
3k views

Multivariable Gradient Descent in Numpy

Just recently started learning ML, first I've gone through the notes of Ng's Coursera stuff. While I have nothing against Octave, I'm trying to solve exercises in Python. It's my beginning with that ...
6
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1answer
375 views

Arbitrary Precision nth Principal Root in Java - MathCore #1

This post is the first in the MathCore series. The next post is here: Arbitrary precision π (Circular Constant) in Java - MathCore #2 Disclaimer My project is too big to be reviewed in a single ...
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0answers
155 views

Calculating Pi to a tolerance

I'm taking my first steps in the Scala world, though I'm not wholly unfamiliar with functional style. Apparently one way of calculating Pi is to sum the terms of the infinite series: $$4 * (\frac{1}{...