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

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5
votes
2answers
122 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
122 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
333 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
500 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
275 views

Spiral roots, how?

I found this picture on the net, as I can play in mathematica
4
votes
4answers
260 views

How can I name “a[[i]]” the parts of Table “a”? Or how to make Table “a” grow inside FindMinimum?

Let's say I want to minimize a function that uses a Table named a with the Conjugate Gradient Method of ...
4
votes
3answers
691 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, ...
4
votes
3answers
1k views

Creating a 3D List Line Plot From Discrete Points

Given the following Runge-Kutta ODE solver and the graphical output below, how do I get a 3D line plot instead of a 3D point plot? I see that there is no ListLinePlot3D function, so I thought it might ...
4
votes
3answers
341 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) ...
4
votes
4answers
1k views

Numerical differentiation methods

Is it possible to write code in Mathematica that implements various differentiation methods (like forward, central, extrapolated, etc.)?
4
votes
3answers
356 views

First 10 digits of $\pi$ without rounding

I need to have $\pi$ with an accuracy of $10$ digits. My first guess would be N[Pi, 10] However, this rounds to the last digit instead of just chopping of any ...
4
votes
3answers
223 views

Increasing the precision of a calculation

Clearly I have misunderstood how to do this: I seem unable to understand how to get more digits out of a calculation and I can't see why - the following piece of code illustrates the issue. ...
4
votes
2answers
198 views

Numerical sum does not give consistent results

Consider the function ...
4
votes
4answers
401 views

How to find the maximum of a function on a set of discrete points?

How to find the maximum of a function on a set of discrete points? For example, what is the best way to find the maximum of ...
4
votes
2answers
579 views

Finding all/most roots of a discontinuous function more consistently?

I have the equation: f[x_]:=α Tan[α*a] - Sqrt[c - α^2] and ideally I want to find all of its positive zeros, given a and c, with variable alpha. The problem is ...
4
votes
1answer
204 views

How do I get a list of digits for a number?

I have this 200 digit number where I want to get the IntegerDigits, but the decimal point is in the way. ...
4
votes
4answers
140 views

RegionMember with some tolerance?

Can I specify some tolerance for the new geometric-computation function? RegionMember[Line[{{0, 0}, {1, 0}}], {.5, 0}] (* True *) While: ...
4
votes
2answers
604 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): ...
4
votes
1answer
435 views

Why IntegerPart[x/(x/2)]=1?

Consider this code x = 0.109354682484; IntegerPart[x/(x/2)] (* 1 *) Precision[x] (* MachinePrecision *) Why does it give 1 ? Version number: 9.0 on Mac 10.9.2 ...
4
votes
2answers
205 views

Graphing convolutions of user defined functions

I am a statistician who is very new to Mathematica. Ultimately I would like to be able to graph convolutions of arbitrary user defined functions. But I can't as yet obtain values of such ...
4
votes
2answers
512 views

Why doesn't FindRoot work correctly?

I'm trying to find the roots of the following equation: I need to find λs for different values of ξ. I know that for all ...
4
votes
1answer
226 views

How to solve this trigonometric system of equations numerically?

How can the following trigonometric system of equations be solved numerically? ...
4
votes
2answers
450 views

Any ideas on how GeneralMiniMaxApproximation is implemented?

GeneralMiniMaxApproximation is used to construct minimax approximations of parametrically defined functions. I am curious about how ...
4
votes
1answer
198 views

Why to do parentheses change the results of a calculation?

I'm getting results that are sensitive to where I place parentheses with respect to operations that are associative1 (and should thus be insensitive to such placement). For example, if I define2 ...
4
votes
4answers
153 views

First digit difference between two numbers

I was trying to build a function that finds the first decimal place difference between two decimal numbers of same sign. An example: ...
4
votes
1answer
423 views

Using NDSolve to solve Equation of Motion in cylindrical coordinates

I have a set of coupled differential equations which represents the equation of motion of a particle in cylindrical coordinates with the following Hamiltonian: $$ H=\frac{1}{2m} \left( p_r^2 + ...
4
votes
2answers
179 views

Floating point addition not associative

Can anybody explain the following behavior? x = 0.2 + (0.3 + 0.1); y = (0.2 + 0.3) + 0.1; x == y (* -> True *) But actually the variables do not exactly ...
4
votes
1answer
106 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
1answer
220 views

Numerical errors/inaccuracies in ProductLog

Context In cosmology, a fairly accurate model to describe the gravitational potential, $\psi(r)$ of dark matter halos is given by $\psi( r)=\log(1+r)/r$. ...
4
votes
1answer
377 views
4
votes
1answer
869 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 ...
4
votes
2answers
173 views

NDSolve in Mathematica won't use all the cores avaiable

When I solve a system of differential equations in Matlab, the task manager shows that all the CPU cores are in use. This is not true when I solve the same system in Mathematica. I have six cores. ...
4
votes
1answer
165 views

Minimize failing on a polynomial

Calling: Minimize[{-0.4877 - 0.1190 r^2 - 0.1885 r^4 + 2.9703 z - 0.5531 z^2, 0 <= z <= 3.5 ∧ 0 <= r <= 1.75}, {r, z}] returns ...
4
votes
1answer
385 views

Is there a way to globally set when to treat a very small number as zero?

I understand that I can use Chop to force a very small number to be treated as 0 and can use ...
4
votes
1answer
87 views

FindFit runs extremely slow for my Function,how do I optimize this?

My function is the first order Bessel Function, and I am basically just trying to get this to fit in a way that does not take forever. I define the function as follows, (it seems to work faster if I ...
4
votes
1answer
214 views

Find lengths of contours in a ContourPlot

I am trying to find the lengths of different contours in the following plot: It is a complicated piecewise function evaluated on the unit disk. I am hoping there is an easy, generalized way to ...
4
votes
2answers
329 views

Quickly reducing the number of decimal digits for a set of real numbers

How can I quickly convert a number with $n$ decimal points to a number of with $m$ decimal points? Round works, however, it is slower than I would like. This ...
4
votes
1answer
115 views

NExpectation not up to expectations with Boole or Conditioned

Context I am interested in computing numerically the number of extrema at a given threshold for random fields. These numbers are expectations of MultinormalDistributions. Problem This integral ...
4
votes
1answer
312 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 ...
4
votes
1answer
158 views

NDSolve - sampling for result during the computation

I am using NDSolve for a Langevin dynamics problem. I want to the know long term behaviour of my system ($t>1$) but it has to be simulated with very small time steps ($dt\sim 10^{-9}$). An example ...
4
votes
1answer
413 views

Counting the number of operations performed during a calculation

I need to know how can I count the number of operations performed during a calculation of a CompoundExpression. In some of these expressions there are ...
4
votes
0answers
954 views

Numerically solving system of partial differential equation

I am trying to solve a system of partial differential equation with boundary conditions. But I got an error message saying NDSolve::icfail: Unable to find initial ...
3
votes
2answers
278 views
3
votes
2answers
528 views

Unexpected result of summation

I wrote small module that gives me incorrect output-set, it should be a single number! I don't understand what went wrong. This is the form of summation used: $$\frac{1}{2} (b-a) \sum_{i=1}^n ...
3
votes
3answers
783 views

How can I solve Tan[t] - t == F[x] for t as a function of x?

How can I solve the equation Tan[t] - t = Ax, where A is a constant for t[x]? I know that ...
3
votes
1answer
391 views

N[number, 100] does not give 100 decimal places [duplicate]

Please look at this computations: a = N[Sqrt[2], 20]; N[a^2, 100] The output is 2.0000000000000000000, which is apparently not $a^2$ to 100 decimal places. ...
3
votes
2answers
254 views

Computing the minimum distance in a contour plot

I have the following Mathematica code ...
3
votes
3answers
275 views

How can I find the sum of the even digits of a number of all elements of a list?

Let $E(n)$ denote the sum of the even digits of $n$. For example, $E(123456789) = 2 + 4 + 6 + 8$. I tried a = IntegerDigits[123456789] and ...