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

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0
votes
2answers
424 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, ...
3
votes
0answers
84 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 ...
17
votes
3answers
339 views

How to flush machine underflows to zero and prevent conversion to arbitrary precision?

I'm working on some pretty intense computation in Mathematica; when my code started running slowly, I tracked the source of the problem to Exp[]. I need to ...
3
votes
2answers
240 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 ...
12
votes
4answers
336 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 ...
0
votes
0answers
20 views

How can I obtain absolute result for Root[ # ] symbol [duplicate]

I'm using mathematica 8.0. When I calculate NDSolve`ImplicitRungeKuttaGaussCoefficients[10, Infinity] function, it gives me some symbolic results. I trided //N and //FuıllSimplify operation as in How ...
1
vote
1answer
118 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
246 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
1answer
142 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} ...
2
votes
0answers
53 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 ...
4
votes
3answers
239 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
69 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: ...
8
votes
4answers
284 views

Numerical instability in cosh and sinh - integral functions

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 ...
1
vote
0answers
269 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 ...
6
votes
3answers
241 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] ...
5
votes
1answer
348 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
118 views

NSolve with numerical function

I would like to solve numerically an equation which involves a numerical function constructed by fitting some data: ...
6
votes
1answer
444 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 ...
13
votes
1answer
143 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 ...
1
vote
1answer
77 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
52 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 ...
9
votes
4answers
329 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. ...
2
votes
1answer
148 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 $\psi( r)=\log(1+r)/r$. ...
6
votes
2answers
296 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: ...
2
votes
4answers
155 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
134 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
83 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
105 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?
5
votes
4answers
333 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 ...
0
votes
0answers
130 views

NMaximize, restart

I have to optimize some contrained functions and I am trying to use NMaximize. I have the following problem (see code below). I use ...
6
votes
1answer
184 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}, ...
1
vote
3answers
120 views

automatic processing of numerical results in `Plot`

First I want to solve an equation $F(x,y)=0$ for $y$ by supplying a value of $x$. (suppose obtaining the analytic form of $y(x)$ is too difficult) Then I want to plot root $y$ (numerically calculated) ...
0
votes
0answers
94 views

Getting increased accuracy for roots of determinant

I have a matrix $a(\kappa)$ from which I am trying to determine $\kappa$ by using the equation $det(a(\kappa)) = 0$. The matrices I deal with are on the order of 100 X 100 to 500 X 500. Originally I ...
3
votes
1answer
305 views

Numerical solution of Bessel-like equation using NDSolve

I need to calculate solution of Bessel-like equation having general form: $\frac{d^2F}{dr^2}+\frac{1}{r}\frac{dF}{dr}+Q(r)F(r)=0$. Problems come from the points near $r=0$ leading to numeric errors. ...
1
vote
1answer
99 views

Passing f[x][[1]] to FindRoot [duplicate]

FindRoot seems to fail for most examples of the form f[x_?NumericQ] := {x - 3 , x^3}; FindRoot[f[x][[1]], {x, 3}] ...
1
vote
3answers
250 views

Can plot a function, NSolve takes too long

I'm new to Mathematica, so maybe mine is an easy to solve issue, but I haven't been able to figure it out. I have a series of linear ODEs I solve using for: ...
2
votes
1answer
223 views

Animated Wave Propagation using Fourier & InverseFourier

This is a continuation off of previous help on the first part of my project: fourier issue arising from input miscommunication Now I want to go one step further in the current code. Here's the code ...
3
votes
1answer
215 views
3
votes
3answers
391 views

Implementing Newton's method

I have this question on coding Newton's method in Mathematica. I have some code to go by but I have no clue if it's computing the functions in the right order. The book is the numerical methods ...
12
votes
2answers
249 views

Why do NumberForm and Round apparently use different tie-breaking methods?

When rounding numbers (for example, rounding a real number to the nearest integer), the "round to nearest" rule is usually used. For example, 1.4 is rounded down to 1 and 1.6 is rounded up to 2. ...
1
vote
1answer
136 views

Using NMinimize Properly

I'd like to find the point on a Bezier curve that's closest to some other point. The tricky thing is that because Bezier curves can loop around, the distance function can have multiple local minima ...
0
votes
0answers
129 views
12
votes
1answer
694 views

Numerical solution of coupled ODEs with boundary conditions

I have to solve the following set of ODEs and just can't get good results using Mathematica $$ r\frac{d}{dr}\left(\frac{1}{r}\frac{d}{dr}A(r)\right)-\xi^2F(r)^2\left(A(r)-1\right)=0 $$ $$ ...
1
vote
3answers
396 views

How many iterations of Newton's method are needed to achieve a given precision?

Consider using Newton's method to solve the equation $arctan(x) = 0$. Using an initial guess of $x_0 = 1/2$ produces a sequence that converges rapidly. After $8$, iterations, $x_8$ is accurate to well ...
7
votes
1answer
83 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 ...
3
votes
1answer
93 views

obtaining real roots of negative numbers in a long expression [duplicate]

I have a complicated symbolic expression which contains many terms like $(a/(a-2))^{1/m}$, where $a/(a-2)$ could be positive or negative after replacement. I only need the real root after ...