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

learn more… | top users | synonyms (1)

0
votes
1answer
111 views

Numerical integration of a three dimensional array

I need to integrate a scalar valued function $f\left(\boldsymbol{x}\right)$ where $\boldsymbol{x}$ is a three dimensional position vector; in other words: $\int_{\Omega} f\left(\boldsymbol{x}\right) ...
8
votes
1answer
465 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 (...
0
votes
1answer
105 views

How to obtain a convergent solution iteratively for a linear system of equations

I am working on a problem that requires an iterative procedure to solve a linear system of equations, the system of equations in matrix form is: $$\underbrace{\begin{bmatrix} r_{11} & r_{12} &...
3
votes
2answers
97 views

Slow application of `Outer` on a matrix

I have some performance issue with the calculation of a gaussian kernel applied to a not-that-large dataset. I'm not very good with performance tuning in Mma and I have the feeling this one could be ...
1
vote
0answers
59 views

Is it possible to circumvent this overflow?

I'm trying to evaluate the following function numerically: $ f(A,B)=\frac{2A\pi ^{5/2} (-1)^B}{(A!)^2B!} \, _4\tilde{F}_3\left({\frac{1}{2},1-A,1-A,1-B\atop \frac{1}{2}-A,\frac{1}{2}-A,\frac{1}{2}-...
1
vote
2answers
115 views

Performance in calculating maximum-likelihood- based estimates

My probability density function is a complicated one for which numerical estimation is necessary. Here my pdf: ...
4
votes
1answer
119 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 ...
0
votes
1answer
321 views

How to force numeric evaluation?

I need to evaluate the PolyLog function at some points, but I'm interested in numeric values. E.g. PolyLog[3, 2.7] works fine, ...
9
votes
2answers
386 views

Solve a PDE over a region defined by a Bezier patch

I am using NDSolve to find the solution to a PDE over an arbitrary domain. The domain is specified by a Bezier patch. ...
11
votes
1answer
354 views

Does NRoots own an abstract counterpart? If not, can we write one?

We know when solving linear algebra equations, despite its abstract syntax, LinearSolve is much faster compared to Solve: ...
1
vote
1answer
215 views

NSolve on bounded domain

I don't expect NSolve[] to be able to obtain all solutions in generalfor example. In principle there should be an algorithm that finds all solution to $f(x)=0$ for $...
8
votes
1answer
228 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 ...
0
votes
2answers
127 views

Derivative after numerical Integration

So I have a function that I want to numerically integrate with respect to temperature, so the integral changes depending on the value of temperature being used as it is one of the bounds. After ...
1
vote
1answer
62 views

Characterising the set of parameters that satisfy a system of non-linear equations

I am looking for a solution to the following problem and could not find an answer so far. I have a quintic equation, $f(x;a,b,c,\cdots)-x=0$, where $x$ is the variable with respect to which I need the ...
0
votes
2answers
162 views

Accuracy and WorkingPrecision

Observe that ...
-1
votes
1answer
80 views

My code of plotting a two-variable function is too slow [closed]

I have a code in which my complicated function to be plotted is F(x,p). I would like to graph it for 5 values of p equal to 10^7, 10^8, 10^9, 10^10 and 10^11 for x values between 0.01 and 0.99. All ...
0
votes
1answer
551 views

Problem with FindRoot applied to functions

I am having difficulty with the error "is not a list of numbers with dimensions..." when using FindRoot (and other numerical routines in Mathematica) to solve equations numerically when the argument ...
1
vote
1answer
126 views

Wrong generalized eigenvalues of large numeric matrices

I've been working on a toy model of a variational method of a Hamiltonian H with an overlap matrix S. The point is that when H and S are small enough, Mathematica gives the correct eigenvalues (≈ -1,-...
0
votes
0answers
27 views

why i cannot get appropriate number with my custom precision? [duplicate]

why i cannot get appropriate number with my custom precision? In[25]:= N[(1 + Exp[-30])/(1 + Exp[-29.9]), 1000] Out[25]= 1. I expect to see a few digits after 1....
1
vote
1answer
205 views

How to properly apply NumericQ or s.th. similar here? - NDSolve inside NMaximize

I wrote a function that numerically solves a given Schrodinger equation and returns replacement rules to obtain the time evolution operator. It looks and is used as follows: ...
3
votes
0answers
171 views

Numerical integration: complicated 2D integral seems to be poorly estimated

In the course of some physics research I've been working on, a very annoying integral has appeared that I'm having difficulty evaluating numerically. Any help you could offer would be greatly ...
3
votes
3answers
189 views

Plot a bunch of lines in 3D from point data

I have a 12*25 array, wherein each entry is of the form $\{x,y,z\}$. So 12 different $x$ values, 25 different $y$ values and 12*15 $z$ values in all. I'd like to plot 12 curves of various $x$ values ...
11
votes
3answers
326 views

Why is (-1.)^2. a complex number

Why (-1.)^2. in Mathematica returns a complex number? It looks like in both C and Fortran it returns 1. Why does Mathematica behave differently than the other ...
10
votes
5answers
334 views

Function for a series of joined slopes

I need a function for a series of joined slopes and my solution feels a bit kludgy. Is there a better way? A list of pairs of transition points and slopes: ...
16
votes
2answers
463 views

Why is my data 10 times slower than random data when doing matrix multiplication

I have some data generated from some program, and it appears that matrix multiplication on these data are about 10 times slower than on some random data: ...
1
vote
1answer
154 views

Efficient method of raising matrix to a variable power?

I have a $2 \times 2$ matrix $A$, where each element is a 12th order polynomial in a parameter $a$. I need to raise this matrix $A$ to the $-t/T$ power, where $T$ is a known scalar (for this instance,...
1
vote
3answers
314 views

Speed up NIntegrate, which takes eigenvalues from another function

I have simplified my problem here, in my actual problem the matrix is much bigger which makes it impossible to find eigenvalues analytically. So, I chose standard BCS problem (2x2 matrix) to ...
3
votes
1answer
98 views

How to make N apply to exponent?

For example, I want to covert y + Sqrt[x] to y + x^0.5, where y and ...
1
vote
2answers
719 views

NDSolve with Explicit, Implicit Euler and Trapezoidal method

I am using Mathematica 9.0 both on Linux and Windows and I would like to integrate the Van der Pol equation numerically using various techniques such as Explicit and Implicit Euler and Trapezoidal ...
9
votes
2answers
1k views

Implement the Bisection algorithm elegantly and easily

Description: Rencently, I have finished my course Numerical Analysis, so I'd like to implement many algorithm that I have learned from that course.By this practice, I hope that I can improve my ...
3
votes
2answers
162 views

WorkingPrecision causes issue in the NIntegrate

I really can't figure out why my code sometimes is not working. My integrals involve two variables (k and kz). The integration ...
1
vote
1answer
104 views

The problem (time) caused by ?NumericQ

In here, I asked a related (similar) question. Using ?NumericQ seems have slowed down the entire calculation. But I now have a more serious problem: ...
22
votes
3answers
776 views

Real Numbers in the Wolfram Language

Epilog: Much of the discussion in the answers below revolves around the distinction between Real as a data type and real numbers as a domain or class of numbers (irrespective of the form in which ...
1
vote
3answers
150 views

How can I use the command `Minimize` of this trigonometric function? [duplicate]

I want to find the minimum of the function $\sin^6 x + \cos^6 x$. I tried Minimize[{Sin[x]^6 + Cos[x]^6, 0 <= x <= 2 Pi}, x] I got {Cos[2 ArcTan[1 - ...
3
votes
1answer
48 views

How shortening argument test when declaring functions?

When defining some functions which depend in many arguments sometimes we need to include question Q constraints to diminish processing time. My question is simple, there is a way to shorten a long ...
10
votes
2answers
1k views

Water Hammer - Numerically solving system of PDEs

I'm trying to use Mathematica to solve the water hammer effect. ...
1
vote
2answers
157 views

Increasing number of decimal places with FixedPoint

I've tried: In[169]:= newton3[x_] := N[1/2 (x + 3/x)]; FixedPointList[newton3, 1.0] Out[170]= {1., 2., 1.75, 1.73214, 1.73205, 1.73205, 1.73205} Of course: <...
0
votes
2answers
161 views

Iteration of NDSolve

I have a problem with iteration of the result of NDSolve. Namely, the following code works fine ...
5
votes
1answer
116 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, ...
0
votes
1answer
83 views

DSolve for first order nonlinear equation is solution numerical or analytical?

Hi I'm new to mathematica so I may have a somewhat trivial question. my code below solves and plots the results of a first order nonlinear ODE. The solutions mathematica gives me contains & and #1 ...
3
votes
1answer
243 views

Breaking out of NDSolve

I am solving a coupled set of differential equations with NDSolve for 6 unknown functions of time. At a certain point in time, the system hits a singular point ...
7
votes
2answers
295 views

Mod[1.2, 0.2] is not equal to zero

Why doesn't the following expression evaluate to zero? In[1]:=Mod[1.2, 0.2] Out[1]=0.2 Edit: This is what I wanted to do: ...
0
votes
0answers
244 views

plotting the stable and unstable manifolds of a difference equation

I have a 2D non-linear system of difference equations for variables x and y defined as follows: ...
0
votes
1answer
243 views

Help Please : Error in plotting the solutions of FindRoot

I want to find the roots of an equation using FindRoot as a function of a real parameter K and then plot the real and imaginary solutions vs. the parameter K. The function I'm trying to find the ...
0
votes
1answer
141 views

Fitting data with inclusion of constraints

How do I find a fit for the dataS (see below) with the constraint that the parameter np is an integer, and that the parameters la+lc = 100. A weak attempt at this is provided below for a specific ...
3
votes
2answers
758 views

NMinimize/NMaximize is unable to generate initial points

Mathematica 10 generates a warning that it is unable to generate initial points for numerical optimization problems. I picked a particularly simple example. The problem goes away when ...
1
vote
0answers
40 views

Apparent issue with derivative of FractionalPart [duplicate]

This issue came to my attention from Math.SE: http://math.stackexchange.com/questions/1015325/is-the-derivative-of-x-on-0-1-always-equal-to-1/1015342#1015342 To summarize, it appears that ...
3
votes
2answers
154 views

How to prevent Round with hided fractions

I found a strange behavior in Round. If we try: ToString[Round[4.811, 0.01], InputForm] we get: 4.8100000000000005 When I expected 4.81 In order to ...
-2
votes
3answers
282 views

Defining an alternative derivative function?

I want to calculate the derivative at a point, but I do not want to use the built-in derivative function D. I began with this definition of the derivative , ...