Tagged Questions

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

420 views

Confused by (apparent) inconsistent precision

$$e^{\pi \sqrt{163}} \approx 262537412640768743.99999999999925$$ E^(Pi Sqrt[163.0]) N[E^(Pi Sqrt[163.0]), 35] NumberForm[E^(Pi Sqrt[163.]), 35] returns <...
2k views

When I can assume that all decimal digits returned by Mathematica are provably correct?

How to Control the Precision and Accuracy of Numerical Results Arbitrary-Precision Numbers Mathematica works with exact numbers and with two different types of approximate numbers: machine-...
2k views

Replace very small numbers by zero in the output of a list

I have a long nested list, but many elements are numbers of order 10^-18 or less, e.g. ...
502 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....
2k views

How to convert a string of number into real numbers without precision loss

I searched and did not find similar answers which can resolve the 'no precision loss' issue. A sample string is: ...
772 views

I want to read a file which contains seven columns of real numbers. Mathematica seems to have a problem with the high precision I need. My code: ...
247 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 ...
357 views

Output precision

I've solved some equations using FindRoot and then computed some values. Now when I print the output, I only get a certain precision {{0.01, 496.983, 61.3147, ...
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338 views

Cannot Get Numerical Results to Match

I try this numerical summation (in two parts) ...
142 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: ...
465 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. ...
750 views

Finding differences between Pi with varying number of decimals

I have the following code In[32]:= N[Pi, 2] Out[32]= 3.1 In[33]:= N[Pi, 1] Out[33]= 3. In[34]:= N[Pi, 2] - N[Pi, 1] Out[34]= 0.*10^-1 Why can't Mathematica ...
175 views

Is it possible to change the precision in Compile?

I'm using Compile to do some numerical calculation and I need high Precision. I was wondering if it is possible to change the ...
126 views

Why NIntegrate is badly-behaved on $J_{\frac{9}{2}}(x)$ by default?

A friend of mine showed me this example: Plot[BesselJ[9/2, x], {x, 0, 1}, PlotLabel -> Style["The integrand seems to be simple", 14]] ...
282 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 ...
83 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?
296 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: ...
144 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 ...
272 views

AccountingForm w/o significant figures

Basically I want to build a chart like something I would do in Excel. It should look like this: Here is the formula I'm using and what I've done so far ...
171 views

Is there a way to get BSplineFunction beyond MachinePrecision?

I have been using BSplineFunction (Mathematica 8) to generate a smooth representation of some data, which I might then do some further processing on. As I ...
249 views

Error computing sum of sum of digits

I've defined a function that computes the sum of the base-b digits of n: DigitSum[n_, b_] := Total[IntegerDigits[n, b]] Then I defined a function that computes ...
180 views

Multiply integrand with -1, and the precision changes?

"After multiplying the integrand of NIntegrate with -1, the Precision of the output will ...
315 views

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A problem about fixed point iteration theory

Description Recently, I have been learning a couse called "Numerical Analysis". The fixed point iteration theory was introducted to solve the ...
339 views

ParallelTable and Precision

I'm using ParallelTable[] to calculate a function over a range of my parameters , ($\omega,\ell$). This seems to be working well (in terms of speed increase) except ...
331 views

Fixed-Point Numbers in Mathematica

I am working with a library that needs input in a Fixed Point notation. Iâ€™d like to figure out a way to convert the floating point results into fixed point representation. The fixed point length is ...
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 ...
139 views

Why has Version 10.3 precision reduced?

In version 7.0.1.0 and versions 10.0 and 10.1 the following is produced: ...
227 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 ...
223 views

Numerical error in Mathieu functions

Consider the MathieuCharacteristicA function, which is a piecewise function according to the documentation. The discontinuity happens at integer number. ...
123 views

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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. ...
139 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 ...
190 views

Padding plot ticks with zeros on the right

I would like to know how can I make a real-valued plot tick pad with a zero to the right of the decimal point on integer values. This is what I have: ...
100 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 ...
65 views

Deferent results depending on the input form of the matrix [duplicate]

Why is it so, N[Eigenvectors[{{1., 0.5, 4.}, {2., 1., 2.}, {0.25, 0.5, 1.}}]] returns: ...
81 views

How to set/adjust Precision for an iterative calculation?

How should I restructure this code? I generate a high-order polynomial poly with integer coefficients, then find roots and divide them out of poly one at a time. ...
88 views

Calculations after NumberForm [duplicate]

As specified in documentation center the functions AccountingForm, NumberForm, etc. are useful only to display numbers in ...
224 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 "...