# Tagged Questions

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

1answer
419 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 <...
2answers
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-...
3answers
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. ...
2answers
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....
2answers
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: ...
1answer
770 views

### ReadList can't read from file containing high-precision Reals

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: ...
0answers
245 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 ...
1answer
356 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, ...
1answer
3k views

2answers
338 views

### Cannot Get Numerical Results to Match

I try this numerical summation (in two parts) ...
1answer
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: ...
2answers
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. ...
2answers
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 ...
1answer
174 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 ...
2answers
125 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]] ...
2answers
281 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 ...
2answers
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?
2answers
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: ...
0answers
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 ...
4answers
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 ...
1answer
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 ...
2answers
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 ...
2answers
180 views

### Multiply integrand with -1, and the precision changes?

"After multiplying the integrand of NIntegrate with -1, the Precision of the output will ...
3answers
315 views

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2answers
509 views

### 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 ...
1answer
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 ...
1answer
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 ...
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 ...
0answers
138 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: ...
1answer
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 ...
1answer
123 views

1answer
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. ...
3answers
310 views

### 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. ...
1answer
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 ...
1answer
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 ...
1answer
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: ...
1answer
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: ...
1answer
88 views

### Calculations after NumberForm [duplicate]

As specified in documentation center the functions AccountingForm, NumberForm, etc. are useful only to display numbers in ...
3answers
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. ...
0answers
79 views

### CharacteristicPolynomial returns 0

I have a following matrix. ...
1answer
116 views

### How can I increase the precision of my computation?

How can I increase precision up to 15 digits for the results (EC, and that of FindRoot) computed below? ...
1answer
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 "...