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

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7
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1answer
872 views

What are the algorithm details of FindRoot?

The Help page of FindRoot says: "by default, FindRoot uses Newton's method (Newton-Raphson) to solve a nonlinear system". But I ...
7
votes
2answers
160 views

Efficient way to obtain values of a function defined by an Integral

Consider the following equation: $$S(q)=\frac{(4 \pi \rho ) \int r (h(r)-1) \sin (q r) \, dr}{q}$$ I want to numerically obtain values for $S(q)$ given that I have data points representing $h(r)$ ...
7
votes
1answer
1k views

Is Abs[z]^2 a bad way to calculate the square modulus of z?

For a numerical quantity z, Abs[z] returns the square root of the sum of the squares of the real and imaginary parts of ...
7
votes
1answer
875 views

Handling failed FindRoot calls

I want to handle FindRoot calls which did not converge (e.g "thrown" error message FindRoot::cvmit) ...
7
votes
1answer
281 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. ...
7
votes
2answers
481 views

Is there any fast way to solve a quadratic matrix equation in Mathematica approximately?

Let the square nonsingular matrix $M$ is a given convergent matrix. What are the best scalar values for $\alpha$ and $\beta$ (in the real numbers domain), at which the following quadratic matrix ...
7
votes
2answers
913 views

Function to subdivide interval into n evenly-spaced points

[This post needs better tags than I could come up with. Edits to the tags would be particularly welcome.] I realize that it is trivial to define a function that takes an interval (i.e. two ...
7
votes
2answers
246 views

listplot very large numbers

Suppose we have the following function: NN = 150; W[n1_] := NN!/(n1 ! (NN - n1!)) (1/2)^n1 (1/2)^(NN - n1) Then we can Plot or Listplot it: ...
7
votes
1answer
182 views

Fractal dimension of a large networked molecular system

I am trying to determine the fractal dimension of this complex biomolecule (figure attached). Any clues as to how this can be done. In trying to determine this quantity, I wonder how its ...
7
votes
2answers
601 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) ...
7
votes
1answer
451 views
7
votes
1answer
99 views

Need a generalization of RootApproximant to recognize linear combinations over algebraic numbers

RootApproximant does a very good job when I need to recognize an algebraic number and when enough of its digits are known (or even when an unlimited number of ...
7
votes
1answer
750 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 ...
6
votes
3answers
457 views

RK4 Gravity Simulator

I have the following RK4 solver which splits the two 2nd order ODEs, used to calculate x and y positions under the influence of a gravitating body where $$x''(t)=\frac{G m ...
6
votes
3answers
284 views

Finding the square root of a squared number?

Taking the square root of the square of a number Variable set to a real value I'm wondering why these examples a = -4.3; Sqrt@a² Sqrt@(a^2) Sqrt[a^2] Sqrt[a²] ...
6
votes
2answers
1k views

how to solve ODE with boundary at infinity

y''[x]-x y[x]==0 y[0]==AiryAi[0], y[infinity]==0 the analytic solution to this ODE is the Airy function y[x]=AiryAi[x] if I ...
6
votes
3answers
230 views

Numerically integrating a list-valued function [duplicate]

I want to NIntegrate a List valued function foo[x] which is only defined for numerical ...
6
votes
2answers
379 views

No builtin function for bitwise rotation?

There appears to be no builtin Mathematica function for bitwise rotation. Is that true? I suppose I can write my function: ...
6
votes
1answer
225 views

How trustworthy is NMaximize?

Suppose I solve a constrained optimisation problem using NMaximize. How confident can I be of the accuracy of the result? For concreteness, suppose that F,G are ...
6
votes
1answer
117 views

Numerical Integration different in Mathematica version 9 and 10 with same options

I have noted that the same function with the same settings gives me different results in Mathematica version 9 and 10. This involves integrating numerically interpolating functions and so on. Here a ...
6
votes
1answer
349 views

Optimizing Monte Carlo simulation of a Pred-Prey model

My assignment and code As part of an assignment for one of my classes, I'm trying to run a "massive" Monte Carlo simulation in Parallel on the follow model: ...
6
votes
1answer
223 views

Iteration process involving several functions

I would like to carry out a following iteration process: Apply function f1[a_,b_,c_,d_] to a starting list l1={a1,b1,c1,d1}, ...
6
votes
1answer
294 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 ...
6
votes
1answer
2k views

Mutual Information involving two matrix states

I basically retrieved the following technique of evaluating the mutual information involving two matrices from this site at http://bmia.bmt.tue.nl/People/BRomeny/Courses/8C080/default.htm The ...
6
votes
0answers
181 views

Mathematica 7: “LessEqual::nord:” error when using NMinimize on a real function

I encounter a problem (Mathematica 7) similar to Strategies to avoid LessEqual::nord in NMinimize? but the advised strategies don't work for me. Also, I get different results with different ...
5
votes
3answers
2k views

Does Mathematica get Pi wrong?

I happened to watch a Youtube video on Pi. According to the video, the 1 millionth digit of Pi is 1. And here is another page of the first 1 million digits of Pi. You can get the same answer from ...
5
votes
4answers
375 views

Display a number in Mathematica 9 in periodic form

I want to display a rational number in Mathematica in periodic style. PeriodicForm isn't working anymore. It worked in Mathematica 5 and now I'm using Mathematica ...
5
votes
4answers
2k views

Numerical Differentiation using 1500 data points

I have a set of 1500 data points (which are some energy eigenvalues) corresponding to a parameter H0 (which represents magnetic field. H0 values are equispaced going from $-3.0$ to $3.0$ in steps of ...
5
votes
1answer
176 views

Why does taking advantage of Listable change the results of a numerical computation slightly?

I have two variables: t0, and teta0. The first is computed using several nested sums, the second is computed taking advantage to ...
5
votes
2answers
102 views

How to speed up Min of DateObjects?

I'm in version 10.0.1 using a Dataset to do some plots and things. For one of the plots I need to get the minimum date of a some filtered set of the ...
5
votes
1answer
100 views

Changing the definition of N: unexpected $RecursionLimit::reclim error

I have some objects represented as follows: Object[data, param] data is a list of numbers, ...
5
votes
1answer
344 views

Is there no documentation for Method in Eigensystem?

There does not appear to be any documentation on how to use Method in Eigensystem, or at least not in Version 9.0.1 of ...
5
votes
1answer
243 views

Accurately evaluating the hypergeometric function

As part of another problem, I am working to evaluate hypergeometric functions such as Hypergeometric2F1[1, 1, n, -1] for large $n$. I am hoping to obtain at ...
5
votes
1answer
1k views

Symbolic integration in the complex plane

Context While answering this question, I defined (symbolic and numerical) path integrations as follows ...
5
votes
3answers
935 views

Solution for equation system with piece-wise defined functions

As I could swear this worked just yesterday, I am probably just doing something stupid here and I am sorry to bother you :) I am trying to find the point where a curve crosses a line. In this case, ...
5
votes
3answers
334 views

Numerical evaluation of a sum

I am trying to compute numerically NSum[(-1)^n/n^3, {n, 1, Infinity}]. Of course, using first Sum would work here, but often ...
5
votes
1answer
82 views

Why is NHoldFirst not propagated to symbolic derivatives?

I encountered a nasty problem that N cannot evaluate expressions containing a symbolic Derivative of a multi-parameter function ...
5
votes
2answers
853 views

Can the CholeskyDecomposition function in Mathematica be made to work on non-symmetric matrices?

The CholeskyDecomposition[m] function in Mathematica requires a symmetric and positive definite matrix m. For instance, the ...
5
votes
1answer
849 views

How can I get Mathematica to allow me to apply FindRoot to an expression that contains NIntegrate?

I am trying to run the following command in Mathematica: FindRoot[NIntegrate[D[f[x], x] / Sqrt[1 - x^2], {x, 0, 1}] - d, {a, 245}] As you might expect, a is ...
5
votes
1answer
111 views

Determining the range of parameters that yield real values for a certain NIntegrate form

I have specified just one set of $s$ and $g$ values that yields a real value for the NIntegrate below. It is possible that some $s,g$ combination can give rise to ...
5
votes
1answer
496 views

p-iteration algorithm to solve Lambert's problem for interplanetary trajectories

I've been reading up on using the p-iteration method to solve Lambert's problem for choosing the correct interplanetary trajectory between two planets given the ...
5
votes
1answer
468 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 ...
5
votes
1answer
282 views

FindMaxValue specifics

I'm using FindMaxValue to study the distribution of maxima of Abs[RiemannSiegelZ[t]] between consecutive values of ...
5
votes
2answers
121 views

Display All Output Numbers in HEX

How might I modify Mathematica such that I can get the following functionality when working with HEX values. The odd lines are input and the even output. Red values should be the HEX values. ...
5
votes
1answer
99 views

How to enforce numerical precision throughout a package

I developed a big package that does quite a bit of numerics. Is there a way to enforce that all numerical computations are done with a pre-defined accuracy? For example, can one use something like ...
5
votes
0answers
120 views

NMinimize seems to call function with the same values multiple times

I have to minimize a function where the evaluation of one parameter set takes very long (around 5sec) and discovered alongside, that NMinimize seems to call this ...
5
votes
0answers
318 views

NDSolve and memory usage

After some googling, i've found similar problems around, but didn't find a 100% satisfactory answer, so let me ask here: I'd like to solve a 1+1 problem using the method of lines. In spherical ...
5
votes
0answers
128 views

Numerical solution of Schrödinger-type equation in Mathematica [duplicate]

I want to solve the following differential equation numerically: \begin{equation} i\partial_{t}\psi(r,t)=\left[-\frac{\Delta}{2m}+g\left|\psi(r,t)\right|^{2}+V_{d}(r,t)\right]\psi(r,t) \end{equation} ...
5
votes
0answers
491 views

Semidefinite Programming

I want to solve a numerical optimization problem using semi-definite programming. Is there a package or add-on that equips mathematica with this functionality?
4
votes
4answers
268 views

Spiral roots, how?

I found this picture on the net, as I can play in mathematica