# Linked Questions

19answers
143k views

### Where can I find examples of good Mathematica programming practice?

I consider myself a pretty good Mathematica programmer, but I'm always looking out for ways to either improve my way of doing things in Mathematica, or to see if there's something nifty that I haven't ...
2answers
5k views

### Determining which rule NIntegrate selects automatically

I need to numerically integrate a highly oscillatory function over the semi-infinite domain $(0,\infty)$: $$\int_0^\infty \frac{\sin^2(x) \sin^2(1000 x)}{x^{5/2}}\mathrm dx$$ Since the Levin rule (...
4answers
1k views

### the winding number for the circle map (Arnold tongue)

I want to perform an iterative calculation and visualize the results: f[n_, a_, b_] := Nest[# + a - b Sin[2 π #] &, 0, n]/n; If I use machine precision, it ...
2answers
1k views

### Obtain approximate Hessian using FindMinimum

According to the documentation, when FindMinimum is told to use the method "QuasiNewton" on a unconstrained problem, it uses the ...
2answers
818 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 ...
3answers
2k views

### NIntegrate-ing a compiled function

I'm trying to integrate numerically in 6 dimensions a very long expression and I read about the option to NIntegrate a compiled function which should be faster. ...
1answer
877 views

### Is there a way to see the result of NIntegrate's symbolic preprocessing?

NIntegrate can do a number of different types of symbolic preprocessing on the integrand before starting the numerical calculations, including changes of variables. ...
2answers
828 views

### Using StepMonitor/EvaluationMonitor with DifferentialEvolution in NMinimize

My question about tracking the progress of a minimisation/fitting process is two-fold: 1. The first part of my question can be considered a slight duplicate/follow-up of this question. There the OP ...
1answer
2k views

### Is this the most effective and efficient programming style for prototyping (a ray tracer) in Mathematica?

I am trying out Mathematica as a prototyping tool. As an initial exercise I have put together a brute force ray tracer, with a view to using Mathematica's built in probability distribution functions ...
1answer
395 views

### ExperimentalNumericalFunction in NMinimize solution

I try to make a number of optimizations using this code: ...
1answer
719 views

### Jacobian of ParametricNDSolve and FindRoot for the Three Body Problem

The main problem I took the time to reformulate the question in a more appealing and concise way. I want to find bifurcations of solutions to the three body problem. In order to do that, I define ...
1answer
758 views

### Preconditioning the objective function of NIntegrate for higher PrecisionGoal

By default, NIntegrate works with MachinePrecision and its PrecisionGoal is set to ...
1answer
255 views

### Is there any way to use compile and still maintain high precision in Mathematica? [duplicate]

Is there any way to use compile and still maintain Arbitrary-precision like 50 in Mathematica?
1answer
124 views

### Is it possible to make listable ExperimentalNumericalFunction?

I have been playing a bit with the undocumented function ExperimentalCreateNumericalFunction and I wanted to know if somebody found a way to make generated ...
1answer
224 views

### How is the Hessian computed using ExperimentalNumericalFunction?

Here and here it was explained how to use Experimental`NumericalFunction to compute the Hessian of a numerical function. I would like to know how this undocumented ...

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