Questions dealing with the relative uncertainty in the values computed, stored, or manipulated by Mathematica.

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4
votes
1answer
96 views

What is a sufficient decrease in the merit function?

As far as I understand, the merit function measures how far the data is from the fitted function. I am calulcating the second partial derivative of a function, and then numerically finding its maxima ...
11
votes
1answer
115 views

Abnormal behavior of RealDigits[x]

In the Details of the document of RealDigits writes the following line: RealDigits[x] normally returns a list of digits of ...
1
vote
1answer
82 views

Nonlinear 2nd order ODE with regular singularities

I am tring to solve the following ODE with NDsolve $2x~(1-x)~f''(x)+(3-4x)~f'(x)+a~f(x)+b~f^n(x)=0;~~a,b\in\mathbb{R},~n\in\mathbb{N}$. The mathematica "code" is: ...
1
vote
1answer
60 views

Behaviour of RealDigits expected or wrong?

Is this behavior expected or a bug? RealDigits[10304.390456] {{1, 0, 3, 0, 4, 3, 9, 0, 4, 5, 5, 9, 9, 9, 9, 9}, 5} when I ...
7
votes
2answers
270 views

NIntegrate fails to converge under almost any PrecisionGoal, MinRecursion etc. How can I trust the result?

I have been getting some ideas by reading other related questions in the forum, but the integral I have to do is not converging in many cases. The integrand is of the form: ...
0
votes
1answer
60 views

Problem with precision of fraction numbers

I have tried to take a series of harmonic numbers using Mathematica and its precision but there has been an issue. So far when I computed the sums at a whole numbers using a precision of 100 digits I ...
1
vote
0answers
71 views

Problem with calculating Harmonic Numbers

I have tried to take a series of Harmonic Numbers using mathematica but there have been issues in calculations. So far when I computed the sums at a small value range such as ...
1
vote
1answer
85 views

Limited Precision calculation in Mathematica

I apologize upfront for the simple minded question, however i couldn't find an answer in either the Mathematica documentation or Stack exchange. I am trying to explore the effect of finite precision ...
3
votes
1answer
74 views

WorkingPrecision in a sum

If I am interested in getting a fairly precise plot of f2 below, can I use WorkingPrecision to do this? ...
4
votes
1answer
42 views

Failure in use of SetPrecision with Filter

I am working with a narrow band filter and I wish to use a high precision version. The filter is defined using Integers with Laplace variable s. Here is the, rather horrific, equation: ...
1
vote
1answer
69 views

Invoking WorkingPrecision slows down Eigenvalue calculation drastically?

Normally, obtaining eigenvalues of random numerical matrices is fast. For instance a generic result looks like ...
1
vote
0answers
74 views

Odd plotting/math issue (could be a precision problem) [closed]

I've got a pretty odd error on a project I'm working on and was hoping to enlist some advice to fix it. The goal of this notebook is to show that I can eliminate the non-normalizable (blowing up part) ...
1
vote
1answer
76 views

Calculations after NumberForm [duplicate]

As specified in documentation center the functions AccountingForm, NumberForm, etc. are useful only to display numbers in ...
3
votes
1answer
56 views

Export followed by Import producing “0.e1” numbers

I had a large table of data that I exported, and then when it had completed, I exported it to a file. (Just in the form Export["filename.dat", data], no specified ...
1
vote
0answers
40 views

Using precision in Mathematica code [duplicate]

I would like to use a specific precision for several different calculations in Mathematica code. I know that using SetPrecision can give you the required precision ...
3
votes
0answers
145 views

Is FindRoot wrong about its WorkingPrecision?

I noticed an odd mismatch between the behaviors of NDSolve and FindRoot. If you give NDSolve an equation of a certain precision, say 20, and tell it to use a higher WorkingPrecision, say 30, it will ...
3
votes
1answer
192 views

How is Precision of Imported Data managed?

I am working on a financial/banking type application and part of the work is to import numeric data of 15 to 20 digits of precision. I am having trouble determining the best way this should be done. ...
12
votes
1answer
269 views

How to add AccuracyGoal and PrecisionGoal options in a numerical function?

There are many built-in functions that contain AccuracyGoal, PrecisionGoal and ...
4
votes
0answers
433 views

Precision and accuracy in NDSolve and NMinimize

I use NDSolve quite a lot and have noticed that setting values for AccuracyGoal and ...
5
votes
0answers
94 views

Is there a problem with some of the curated Star Data?

I'm not really sure if I'm doing something wrong, or if there's a problem with some of the Mathematica curated data on stars. My problem is this: I'm trying to find the location (latitude and ...
0
votes
1answer
54 views

If statement for evaluating small values

I have a simple calculation which I am trying to use if condition to evaluate summation of some values, here's a code; ...
5
votes
1answer
84 views

Can Someone Please Explain Internal`$SameQTolerance?

If I input Internal`$SameQTolerance (* output = 0.30103 *) which is the approximation of Log[10,2], or ...
2
votes
1answer
47 views

Integrate and NIntegrate combined, giving MaxPrecision error

I am trying to integrate the following : ...
0
votes
0answers
18 views

Increasing the zero threshold [duplicate]

I have a function similar to this: func[x_]:=Log[1+x] when I evaluate it at very small arguments, it will become 0, i.e. ...
5
votes
1answer
141 views

Inaccurate Heliocentric coordinates of PlanetaryMoonData

I have noticed that the heliocentric coordinates obtained with PlanetaryMoonData are very inaccurate. Fore example, consider the Galilean moons of Jupiter: ...
1
vote
1answer
220 views

Precision while calculating Fourier transform

I'm trying to understand how precision works in Mathematica. Particularly I'm calculating discrete Fourier transform using the Fourier function and calculating it "...
1
vote
0answers
78 views

CharacteristicPolynomial returns 0

I have a following matrix. ...
17
votes
0answers
235 views

Is MathieuC for moderately large imaginary arguments broken?

I'm trying to plot MathieuC[-3,0.3,I x] for $x\in[0,10]$, and here's what I get even with arbitrary precision arithmetic (here I use ...
0
votes
1answer
39 views

Precision digits in Log[] [duplicate]

Why does N[Log[10, 6613], 20] give the requested 20 digits of precision (* $3.8203985227039816648$ *) but ...
1
vote
1answer
41 views

Generation of list of values for small gap among values

I need to run a loop as Table[expr,{i,imin,imax,di}] where I want di to be as small as order of ...
5
votes
1answer
166 views

FindMinimum's WorkingPrecision behaviour

I discovered the following behaviour when using FindMinimum for constrained optimization: ...
0
votes
1answer
55 views

Fine precision control in IntervalSlider

I would like to develop a simple slider for exploring a wide range of intervals on the real line. Is it possible to get the MinimalSize of IntervalSlider to work ...
2
votes
2answers
284 views

How to get the digits after the decimal point

I have N[Sqrt[2], 8] which outputs 0.4142136 How do I get the 4142136 part out of it? I ...
0
votes
2answers
82 views

Why is Sin[2.0 Pi] = -2.44929 x 10^-16 and not 0.0?

Why does Sin[2.0 Pi] evaluate to -2.44929 x 10^-16 and not 0.0?
5
votes
1answer
133 views

Specifying WorkingPrecision in LogLogPlot produces invalid plots [duplicate]

I seem to have found a bug with LogLogPlot in Version 10. If I specify a working precision, the function produces total garbage. Here is a simple example. The first ...
2
votes
0answers
61 views

Precision loss in FourierDCT

I have high precision data that I want to do Fourier transform with, but it looks like the precision is lost dramatically. ...
-1
votes
1answer
183 views
1
vote
0answers
155 views

How to control precision of parameters in NonlinearModelFit?

I am using NonlinearModelFit for fitting a dataset to some complex numerical model function that depends on a few parameters. The final required precision of these parameters is very low, like 3 ...
3
votes
1answer
227 views

Precision of NIntegrate

At the moment I am considering a "difficult", highly-oscillatory integral in Mathematica. It calculates the integral without any complaints. However, I am also trying out a numerical method with which ...
8
votes
1answer
221 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 ...
2
votes
3answers
229 views

NSolve & PrecisionGoal

I am using NSolve to find numerical solutions of a particular equation. I do not need the solutions to as high of a precision as the other numbers in my notebook. To improve run time (I am iterating ...
0
votes
2answers
156 views

Accuracy and WorkingPrecision

Observe that ...
1
vote
1answer
118 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
26 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....
3
votes
2answers
461 views

Permanently rounding numbers/values to a given number of significant figures

I am searching for a simple way of rounding and setting an input to a desired number of significant figures. There are a vast number of posts that discuss similar problems, but none address this issue....
5
votes
1answer
125 views

Is the divergence between Round and setting an explicit precision intentional or a bug?

Introductory remark: I take it (from Mathematica's online documentation), that Precision is effectively the number of significant digits, as seen by the system. ...
3
votes
1answer
41 views

Is it possible to generate a message when precision upgrade occur?

I use Mathematica mostly for numerical simulation, so most of the time double precision (or machine precision) is enough for me. Mathematica has this nice feature of automatically upgrade to arbitrary ...
0
votes
2answers
77 views

Failed to use SetPrecision

I am calculating the below formula: $$ \text{ER2}(\alpha,\text{K},\text{q})\text{:=}1+\sum _{m=0}^{K-1} \binom{K+\alpha }{m} \sum _{r=0}^m \frac{(-1)^r \binom{m}{r}}{\left(\frac{1}{q}\right)^{\alpha +...
0
votes
1answer
153 views

Why is chop being ignored? [closed]

If I use Chop[10^-4, 10^-3] then I'd expect the output to be zero. However, this is not the case. There is of course a very easy workaround since I can define ...
4
votes
2answers
273 views

Explicit digit-count (precision) of real number

I'm trying to do something which seems like it should be simpler than it is (at least in my attempts at it). I have some code where I read in a list of numbers generated for me by a coworker. These ...