Questions on the numerical functions of Mathematica, implementing numerical methods and numerical computing with Mathematica.

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0
votes
1answer
146 views

Numerical rule evaluation -> {True, False} to deviation of target equation

I solve some equations numerically with FindRoot[] returning a quadruple {1,2,3,4}. Because the solver sometimes do not find any roots depending on parameterization of these equations I select only ...
6
votes
1answer
315 views

Numerical problems with calculation of function

I have a problem with a calculation which I try to do with Mathematica (8.0.1). I have the following function which describes a cone (with half opening angle ...
31
votes
8answers
7k views

About multi-root search in Mathematica for transcendental equations

I have some questions for multiroot search for transcendental equations. Is there any clever solution to find all the roots for a transcendental equation in a specific range? Perhaps ...
11
votes
2answers
558 views
15
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3answers
2k views

Finding a fit to a multi-dimensioned function

I have a model function $f:\mathbb{R}^2\rightarrow\mathbb{R}^2$, and a bunch of data points for which I'd like Mathematica to fit for me. Unfortunately FindFit ...
4
votes
3answers
778 views

Output of NonlinearModelFit differs from the correct result

I'm having a bad time dealing with the NonlinearModelFit in Mathematica 8, since the result given is a bit imprecise. An example is given on potential regression, ...
0
votes
1answer
380 views

Tabulating Numeric Approximation

I was wondering how to approximate or tabulate values for this numeric approximation: It is the following: The confusing part is how to implement the subscripts in mathematica. $y_{i+1} = (t_i - ...
11
votes
2answers
4k views

Numerically obtaining the inverse Laplace transform of data

I have been using several Mathematica packages to do numerical inverse Laplace transforms on known (expressible in closed form) expressions, $\tilde{f}(s)$. I am now being confronted with the more ...
17
votes
3answers
4k views

Solving a Volterra integral equation numerically

I would like to solve for $P(t)$, in Mathematica, a Volterra integral equation of the 2nd kind. It is: $$P(t) = R_0(t) + \int_0^t P(t') R_0(t-t')dt'$$ I know the function $R_0$ and would ...
8
votes
2answers
890 views

Number of iterations in NSolve

In Excel's solver, one can define how many iterations are to be done, to one's liking. I am wondering if this is possible to do with NSolve in Mathematica? Code ...
39
votes
6answers
7k views

Finding real roots of negative numbers (for example, $\sqrt[3]{-8}$)

Say I want to quickly calculate $\sqrt[3]{-8}$, to which the most obvious solution is $-2$. When I input $\sqrt[3]{-8}$ or Power[-8, 3^-1], Mathematica gives the ...
15
votes
4answers
2k views

Numerical underflow for a scaled error function

I calculate scaled error function defined as f[x_] := Erfc[x]*Exp[x^2] but it can not calculate f[30000.]. ...
18
votes
6answers
2k views

Annoying display truncation of numerical results

I have a lot of data to inspect. An example of a number in my program is 123.189094 This gets displayed as 123.189 ...
8
votes
1answer
1k views

Handling failed FindRoot calls

I want to handle FindRoot calls which did not converge (e.g "thrown" error message FindRoot::cvmit) ...
20
votes
2answers
776 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 ...
12
votes
2answers
394 views

Wrong computation with N

I was trying to solve this problem using Mathematica 8.04. I did this: ...
27
votes
3answers
1k views

Funny behaviour when plotting a polynomial of high degree and large coefficients

I am trying to plot a polynomial of degree $29$ on the domain $[0,1]$, with fairly large coefficients: ...
28
votes
2answers
2k views

Meaning of backtick in floating-point literal

If I compute, say, 1/3//N, Mathematica displays 0.333333 as the result. When I copy that output to use elsewhere, the paste ...
5
votes
3answers
381 views

How to cancel floating point factors?

I am currently having problems with some floating points. I have a function, which gives as an intermediate result (for example) ...
31
votes
1answer
1k views

Numerics with Mathematica

From time to time, I would like to use Mathematica purely numerically, e.g., plotting a function which is defined as an integral which cannot be solve analytically or a solution of a differential ...
42
votes
3answers
13k views

Why round to even integers?

According to the Mathematica help: Round rounds numbers of the form x.5 toward the nearest even integer. For example: Round[{0.5, 1.5, 2.5, 3.5, 4.5}] ...
13
votes
2answers
1k views

Is it possible to use the LevenbergMarquardt algorithm for fitting a black-box residual function?

I have a black-box multiargument multiparametric function of the type SRD[dataPoint_List,params_List] which accepts experimental data along with the parameters of ...
9
votes
2answers
1k views

RootSearch for complex or multiple equations

First the background. I'm trying to solve for the roots of a rather messy complex equation. This is not the exact equation, but it's a decent (simpler) stand in: ...
8
votes
1answer
687 views

Is there any automatic differentiation package?

I'm wondering if an automatic differentiation package exists for Mathematica. This is what I mean by automatic differentiation.
13
votes
1answer
2k views

Kramers-Kronig in Mathematica

I am trying to calculate the change of the refractive index from the change of the absorption coefficient using the Kramers-Kronig relations, in Mathematica. ...
16
votes
1answer
3k views

Parallelizing Numerical Integration in Mathematica

I have an ugly, six dimensional function that I need to integrate numerically. It works, but it currently take twelve hours to complete the calculation. Is there any good way to parallelize the ...
7
votes
2answers
680 views

How to apply restrictions to the “integrated” variable, when using NDSolve?

I have to integrate an energy along a path. I know the energy at the "beginning" of the path (energy[0]), and I can determine the energy change (gain and loss) ...
4
votes
1answer
326 views

How to fix errors in Gram-Schmidt process when using random vectors?

I first make a function to get a random vector on unit sphere in a swath around the equator. That is what the parameter $\gamma$ controls; if $\gamma = 1/2$, the vectors can be chosen anywhere on the ...
15
votes
1answer
475 views

Why is MainEvaluate being used when LinearSolve can be compiled?

According to this question LinearSolve can be compiled. However, CompilePrint[] shows a call to ...
4
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1answer
1k 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 ...
7
votes
1answer
988 views

Using Mathematica to help to determine the consistency of and numerically solve systems of non-linear equations

The formal problem The question I am about to ask is applicable to many scientific and engineering problems. In short, I am bout to ask for pointers and practical advice for Mathematica beginners who ...
14
votes
3answers
1k views

Strategies to avoid LessEqual::nord in NMinimize?

When using NMinimize on functions with complex intermediate expressions (but a real end result), quite often one gets the error ...
25
votes
4answers
2k views

How to use NDSolve to track equilibrium?

I am looking for an extension of NDSolve where integration runs until certain variables are settled at an equilibrium. Now I have a working solution in my sleeves ...
14
votes
1answer
595 views

How to guarantee that NDSolve correctly detects abrupt changes in parameters?

When using NDSolve, I often have parameters that, in most of their domain, have a constant or null variation, but that suffer from abrupt variations on a very small ...
12
votes
1answer
2k views

Combined numerical minimization and maximization

I want to numerically calculate the maximum of a function defined by the minimization of another function, like the following: ...
57
votes
9answers
3k views

Updating Wagon's FindAllCrossings2D[] function

Stan Wagon's Mathematica in Action (second edition; I haven't read the third edition and I'm hoping to eventually see it), demonstrates a nifty function called ...
43
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 ...
21
votes
1answer
404 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 ...
48
votes
10answers
3k views

Can Mathematica propose an exact value based on an approximate one?

Sometimes, I use Mathematica to do some hypothesis on homeworks to make the question easier. For instance, when I have to compute big sums when $n\to\infty$ and Mathematica can't give the exact ...
23
votes
2answers
528 views

Symbolic derivatives are being calculated numerically

Just found the following while debugging a problem. Mathematica is calculating the derivative of IntegerPart[x] in some odd way: ...