# Questions tagged [numerical-methods]

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

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### IEEE 754 square root with Newton-Raphson

I have an implementation of the sqrt function that uses a combination of IEEE 754, packed bitfields, and the Newton-Raphson algorithm: ...
975 views

### Mean π: Archimedes vs. Gauss - π computation through generalized means

I've written this simplified code to compute Pi for educational/demonstration purposes. These methods are based upon the generalized means: see a presentation on Pi and the AGM. Archimedes' method ...
57 views

### Arbitrary precision Euler-Mascheroni constant via a Brent-McMillan algorithm with no math module

Utilizing the below relation, I am able to compute the Euler constant to great precision on a single thread quickly and simply. My process is to compute the natural log via the AGM(utilizing Pi an ...
41 views

### Euler-Mascheroni Single Thread Speed Improvements

The below code was written to generate γ, for educational purposes. My general methodology is as follows: Compute Gamma via the accepted answer's algorithm here. In order to do this I need to ...
64 views

### Calculate the Euler-Mascheroni constant without the math module

The below code was written to generate γ, for educational purposes. Single threaded, no functional zeroes required, no binary splitting(which can all be used to compute competitively like y-cruncher, ...
7k views

### Prettify math formula in code

I have a function to calculate the normal distribution in Python: ...
62 views

### Trapezoidal rule for set of data

Here is the question from the book of Mark Newman-Computational Physics Exc 5.1 a) Read in the data and, using the trapezoidal rule, calculate from them the approximate distance traveled by the ...
101 views

946 views

### Bisection to find roots in C++

I have written a short C/C++ code finding root by bisection. (This is a simple iterative numerical method allowing to find the root of an equation i.e. x such that f(x) = 0). Bisection Method The ...
268 views

### 2d linear Partial Differential Equation Solver using finite differences

This is code that solves partial differential equations on a rectangular domain using partial differences. fd_solve takes an equation, a partially filled in output, ...
91 views

### Calculating Maclaurin series for sin(x)

I'm very new to Haskell as was hoping to get some feedback on my code AND I have some specific questions. I've posted code below or you can see it here. I'd welcome ideas on how better to calculate ...
4k 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 ...
2k views

### Definite Integral Approximation using the Trapezoidal Method

I wrote a program to calculate the value of Definite Integral of a function from a to b. It used the trapezoidal approximation ...
211 views

### Numerical integration with Numba

I'm a bit new to working with Numba, but I got the gist of it. I wonder if there any more advanced tricks to make four nested for loops even faster that what I have ...
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. ...
605 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 ...
78 views

### A single function for implementing Newton forward and backward polynomial interpolation

On various websites, I've come across a lot of realizations of Newton polynomial interpolation that use separate functions for forward and backward interpolation, respectively. Such solutions seem ...