2
votes
1answer
114 views

How can I reduce computation time while still obtaining a good approximation for my function?

I am new to any CAS (and Mathematica, for that matter) and new to StackExchange too, so forgive me and correct me on any mistakes. I have this function: $J_p=\sum_{m,n=1}^{\infty} ...
17
votes
1answer
279 views

How to work with Experimental`NumericalFunction?

This question is intimately connected with previous one: "How to create internally optimized expression for computing with high WorkingPrecision?" Oleksandr R. correctly states in the comment: A ...
65
votes
2answers
736 views

Why are numeric division and subtraction not handled better in Mathematica?

There is something that has been troubling me for a while. At least in version 7, the performance of a / b and a - b is not ...
4
votes
1answer
104 views

Strange behavior of Mathematica regarding calculation time

Today I witnessed the following strange behavior of Mathematica, when it comes to calculation time involving larger nested lists. The following is the short example that I setup, I am sure one can ...
4
votes
2answers
365 views

Numeric calculation of Hessian

I want to calculate the Hessian matrix for a function that can only be evaluated numerically. So far, I have the following (where f is just for testing): ...
-1
votes
2answers
274 views

Performance of numerical optimization with triple integral [closed]

I'm trying to solve a numerical optimisation that looks something like this: ...
2
votes
0answers
158 views

Speeding up a numerical constrained quadratic optimization

I'm trying to solve a quadratic optimization problem in 35 variables, $\vec{α} = \left< α_1, \ldots, α_{35}\right>$: $$ \begin{aligned} &\operatorname*{maximize}_\vec{α}&&1.0\cdot ...
14
votes
1answer
227 views

How to create internally optimized expression for computing with high WorkingPrecision?

I have large dataset and need to fit rather complicated function on it with different values of one of its parameters (this parameter must be fixed in every fit). I use the ...
17
votes
3answers
347 views

How to flush machine underflows to zero and prevent conversion to arbitrary precision?

I'm working on some pretty intense computation in Mathematica; when my code started running slowly, I tracked the source of the problem to Exp[]. I need to ...
17
votes
1answer
1k views

Optimizing a Numerical Laplace Equation Solver

Laplace's Equation is an equation on a scalar in which, given the value of the scalar on the boundaries (the boundary conditions), one can determine the value of the scalar at any point in the region ...
15
votes
4answers
408 views

How to remove duplicates from set of machine precision 2D points?

I have a set of 2D points with machine precision coordinates. I need to remove all duplicates. Performance is important. This is the most obvious fast solution: ...
2
votes
1answer
386 views

How to solve simultaneous equations faster with Compile?

I have large 6x6 matrix Uwhich is a multiplication of 15 rotational matrix. All of the elements are Sin\[theta] and ...
15
votes
0answers
591 views

Fast Spherical Harmonics radiative transfer

This is a rather specific question and I apologize for spamming you with some lengthy code. But it could be interesting for some reader and maybe you can help out, so please bear with me. I am using ...
5
votes
1answer
375 views

Tridiagonal symmetric matrix eigenvalue using bisection

I know that Eigenvalues is already quite well implemented in Mathematica, nor am I foolishly trying to improve on it. In order to improve my programming skills, I ...
4
votes
1answer
689 views

MaxSteps and Computing time issue for Solving Differential equation in Mathematica

When we solve differential equation numerically using NDSolve then sometimes we get error like NDSolve::mxst: Maximum steps reached According to Mathematica docs ...
35
votes
1answer
2k views

Adaptive sampling for slow to compute functions in 2D

EDIT: Although I have posted an answer based on my current progress, this in incomplete. Please see the "open issues" section in the answer. Most plotting functions in Mathematica adjust the ...
18
votes
1answer
334 views

Is there an NDSolve`ProcessEquations analog for NIntegrate?

NDSolve has an interface for repeatedly solving an equation with different initial conditions without having to analyze the equation and set up the solving algorithm each time. This can improve ...