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

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0
votes
1answer
143 views

Fixed Point Math in MMA

I am working with a library that needs input in a Fixed Point notation. I’d like to figure out a way to convert the floating point results into fixed point representation. The fixed point length is ...
3
votes
1answer
82 views

Why is left NumberPadding always applied in NumberForm?

I would like to display numbers like 9.0001 and 10.0001 in the fixed-width form of xx.xxxx. ...
5
votes
1answer
345 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 ...
3
votes
1answer
386 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. ...
-1
votes
1answer
270 views

Multiple NIntegrate (again)

Basically I have the same question as here: Multiple NIntegrate but since I don't have enough "reputation" I cannot comment there. I want to solve the following multiple Integral numerically at given ...
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 ...
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: ...
2
votes
1answer
364 views

Numerical Integration with Variable Parameters

So I want to numerically compute the integral of a long complicated expression over a specified domain (in this case an ellipse). I know how to use a Boole function to sample within the ellipse, but I ...
3
votes
0answers
279 views

How to determine BLAS/LAPACK implementation used internally for numerical matrix operations?

Is there a command which reveals which implementation of BLAS and LAPACK are used in Mathematica's matrix operations such as Eigensystem? I asked a related question ...
1
vote
1answer
248 views

Numerical saddle point problem of a function of many variables

I want to find the following saddle point of the function of 10 variables: . I am not able to find the stationary points by setting the first derivatives to 0, so I need do optimize the function ...
1
vote
3answers
111 views
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. ...
1
vote
1answer
115 views

Find Numerical Derivatives (With Errors) given some data

I have a question. Suposse I have some data with their respective errors: ...
1
vote
0answers
97 views

NMaximize and Accuracy

I have a problem with NMaximize which is best depicted by the following figure. The result indicates, that the solution mathematica finds seems to be smooth except a few outliers. How can I get rid of ...
75
votes
1answer
1k views

Why are numeric division and subtraction not handled better in Mathematica?

There is something that has been troubling me for a while. At least through version 10.0 the performance of a / b and a - b is ...
0
votes
1answer
423 views

How to use NIntegrate in a function using parameters from a list

I would like to use NIntegrate in a function with some parameters from a list. I simplified my problem for this forum. The list of parameters is as follows: ...
4
votes
2answers
200 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 ...
0
votes
2answers
214 views

FindMinimum gets confused by If[…]

I'm confused by why the following doesn't work. I'm trying to numerically minimize a function that has an If statement in its definition, as follows: ...
3
votes
0answers
100 views

Tools for Stability/Automatic Error Analysis in Mathematica

I have a longer analytic expression in several variables containing special functions and others. Does Mathematica bring tools - or are there any packages - to examine the stability when I evaluate ...
3
votes
2answers
178 views

Solve-ing with initially unassigned parameters and Solve-ing using their numerical values produces different results

I am trying to solve an equation using the following piece of code: ...
2
votes
1answer
132 views

Decomposing a diagonal positive real matrix

I would like to 'decompose' a diagonal positive real matrix $E$ of rank $D$ onto $\sum_{i=1}^{D}c(i)N^i$: $$E = \left( \begin{array}{ccc} 0 & & & \\ & a & & \\ ...
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 ...
1
vote
2answers
668 views

Kramers Kronig Relation for Phase and Complex Reflectivity

I am a new user to Mathematica and I have been trying to figure out how to find $\Theta(\omega)$ from my 'experimental' values of energy and $\ln(\sqrt{R(\omega)})$ (I am just running a simulation, ...
12
votes
4answers
436 views

Elegant high precision `log1p`?

Sometimes it is hard to understand how numerical expressions are evaluated. I remember reading claims by Wolfram on how smart the Kernel is to evaluate expressions trees numerically by recognizing ...
1
vote
1answer
183 views

Perform FindRoots on Function Evaluation Containing RootSearch

I am using Ted Ersek's RootSearch function in Mathematica 9.0 (http://library.wolfram.com/infocenter/Demos/4482/) to create a function that I am using for graphing. ...
1
vote
1answer
164 views

Problem to solve an integral equation [closed]

I am new to Mathematica. I am trying to numerically solve for C in the following equation: $\begin{equation} \begin{array}{lcl} -\int_0^\infty (5000000+100000 x+ C)^{-1} ...
3
votes
0answers
77 views

Understanding NDSolve::ndsz

I'm working on a largeish system of differential equations where I encounter the NDSolve::ndsz step size is effectively zero; singularity or stiff system suspected ...
2
votes
2answers
87 views

Forcing RecurrenceTable + NIntegrate to evaluate lazily

I have a recurrence relation that grows exponentially if expressed in closed-form. I need to integrate this function. If I plot it, I think Mathematica evaluates the recurrence numerically at every ...
2
votes
2answers
301 views

Can Mathematica identify formulae or sequences of numbers?

Can Mathematica suggest what a formula means? For example if I input $$\sum_{i=0}^n i$$ can it infer that this is a sum of integer values from $0$ to $n$? Or if I enter $0,1,1,2,3,5,8,13$, can ...
4
votes
3answers
354 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 ...
2
votes
1answer
87 views

Convert Integer to Numeric with Replacement rules

I have a long list of triples, each looking something like {AGO, 1988, 2345.23}. Some of these, however, have an integer in the third spot, like this: ...
1
vote
0answers
514 views

DSolve 2nd Order Coupled Partial Differential Equations

I am trying to use Mathematica to solve 2 coupled differential equations. My equations are of the form \begin{equation}\ddot{x}_i + A_{il} \partial^l A^{jk} ( \dot{x}_b \dot{x}_c - y_b y_c ) =0 ...
8
votes
4answers
357 views

Numerical instability in cosh and sinh - integral functions [duplicate]

I'm trying to calculate the function: CoshIntegral[x] Sinh[x] - Cosh[x] SinhIntegral[x] Unfortunately Mathematica seems to hit a point (x~20) and things become ...
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] ...
1
vote
1answer
185 views

NSolve with numerical function

I would like to solve numerically an equation which involves a numerical function constructed by fitting some data: ...
7
votes
1answer
873 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 ...
14
votes
2answers
171 views

CompiledFunction returns machine numbers smaller than $MinMachineNumber

When thinking on the workaround for this LogLogPlot bug suggested by halirutan I noticed that CompiledFunction actually can ...
5
votes
1answer
497 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 ...
1
vote
1answer
109 views

How do I get Nsolve to work with hyperbolic functions?

This is a rather simple numerical solution, but it simply doesn't work. Does anybody have a solution? NSolve[x - Sinh[x] - 1 == 0, x] NSolve::nsmet: This ...
0
votes
1answer
84 views

Removing numerically vanishing complex part within NDSolve

I am using functions that are only well-defined for real values (e.g. HeavisideTheta) within NDSolve. Internally ...
11
votes
4answers
494 views

Why is Poisson Random Deviate Generation so slow?

I am generating Poisson deviates for some numerical work. Mathematica 9.0.1 is very slow in generating these random numbers, as can be seen below. ...
4
votes
1answer
217 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
362 views
2
votes
4answers
217 views

Padding and formatting within BaseForm

I find using BaseForm to be a little tricky. For example, if you use BaseForm and then do some additional operation all the numbers turn back into base 10, so you have do BaseForm as the "last step". ...
2
votes
2answers
165 views

Incorrect numerical derivative of function that uses FindRoot

I am trying to plot the derivative of function g[x] below where g[x] is defined as the root of another equation. However, I am ...
0
votes
1answer
97 views

Truncate a fractional value to particular number of bits?

If I have a fractional value, how can I truncate (not round) that to a certain number of bits, like 8? For example, for Pi 3.141569265359... the fractional part is 0.141569265359... ...
2
votes
1answer
182 views

Read C-formatted hexadecimal numbers?

I have a lot of 32-bit numbers in hexadecimal symbolized as they are in C (for example, 0x1230abde). How can easily read these in Mathematica?
6
votes
2answers
380 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: ...
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 ...
6
votes
1answer
224 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}, ...