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

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0
votes
2answers
38 views

Convergence Problem in NIntegrate

I need to evaluate the following integral numerically for different values of a: ...
1
vote
1answer
43 views

Control data type (or precison?) to limit memory usage

I couldn't find the answer to my question, so here it is: I have quite a large table, which I generate in Matlab (for some reasons i use both Matlab and Mathematica, I'd like to use only one of them, ...
3
votes
1answer
125 views

Machine-Precision and Arbitrary Precision [on hold]

What is meant by a machine number in the Mathematica documentation? What is the difference between machine-precision and fixed-point precision? What is arbitrary precision?
16
votes
0answers
176 views

Is manual adjustment of AccuracyGoal and PrecisionGoal useless?

This is a problem confusing me for years. AccuracyGoal and PrecisionGoal are two options that I never truly understand and, to ...
2
votes
0answers
29 views

Use of AccuracyGoal & MachinePrecision in NIntegrate

I just learned about the Inverse Symbolic Calculator and it seems like a very useful tool. For example, to find an analytic solution to $$ \int_0^{\infty } \frac{1-e^{-x} (x+1)}{\left(e^x-1\right) \...
3
votes
1answer
79 views

Precision of FindRoot

Consider the following code: ...
0
votes
2answers
156 views
3
votes
1answer
115 views
11
votes
2answers
119 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]] ...
0
votes
1answer
33 views

SetPrecision on a decimal gives imprecise result [duplicate]

I noticed that SetPrecision doesn't actually guarantee that my number is as precise as I want: ...
1
vote
1answer
53 views

ParallelTable local variables don't update precision

I'm finding that precision of variables updated outside ParallelTable don't update inside of it the way I'd hope. Here's the minimal code that demonstrates my point: ...
5
votes
1answer
73 views

FunctionInterpolation produces many error messages when given high-precision input [duplicate]

Both FunctionInterpolation[1, {x, 0,1.00000000000000004}] and FunctionInterpolation[1.00000000000000004, {x, 0, 1}]; ...
3
votes
2answers
460 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....
1
vote
0answers
37 views

Why doesn't N[0.33333, 3] return 0.333? [duplicate]

Basic question, other answers I found didn't really seem to address this. N[x,3] seems to only work if x is analytic instead of ...
0
votes
0answers
30 views

Analogue maple's Digits Environment Variable [duplicate]

I want setup (in Mathematica) once and for all operations number of digits after decimal point, similar how it's done in maxima: ...
4
votes
1answer
84 views

How can I completely discard decimals after a set number of significant figures?

I have a number with a long decimal tail, like x=1.23456789789456123 and I would like to (i) keep the first $n$ significant figures, and (ii) completely discard ...
7
votes
2answers
175 views

Multiply integrand with -1, and the precision changes?

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

Passive Transformation does not return the expectedt result due to precision of expressions

So I wish to perform a passive rotation in N dimensional space. Let me take N=5 for this question. ...
2
votes
1answer
118 views

Mathematica Precisions vs Doubles in C/C++

I'm having a bit of an issue regarding numerical precision and I'm not sure how to deal with it. I have a certain randomly generated matrix, say $M$, that I wish to compute the eigenvalues. The ...
4
votes
1answer
350 views

How to calculate accurate answer in Mathematica?

I accidentally discovered for myself, that Mathematica outputs inaccurate answer. For instance, if I take $\sin(2 \cdot \pi \cdot 0.5) = 0 $, then in Mathematica it is: But if I calculate it on ...
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
60 views

Precision in calculation [duplicate]

I am writing some code to demonstrate the effect of the number of significant figures a coefficient has on the solution of a nonlinear equation. I define the coefficient as follows: ...
2
votes
3answers
193 views

What's the proper way to 'cut out' an irrelevant part of an integral, so I don't run into problems with precision?

I'm doing a numerical integration that involves an integrand with a few exponentials whose values over the integration region range enormously. I'm really only interested in the part of the range that ...
3
votes
1answer
50 views
1
vote
0answers
56 views

Artifacts in the solutions of NSolve [closed]

I have (what I think are) some problems with the precision of NSolve. I'm trying to solve this cubic equation: $a f^3(x)-b f^2(x)-c f(x)-z=0$ for the function $f(x)$ and then plot the following ...
1
vote
0answers
44 views

Numerical Integral with Boolean as part of argument

I am trying to numerically calculate a partial surface area integral of an oblate spheroid in spherical coordinates. The area I want to calculate is determined by a boolean function in the argument of ...
1
vote
1answer
41 views

How to preserve real number's precision

RealDigits[523.502] gives me {{5, 2, 3, 5, 0, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9}, 3}. Is there a way in run time to tell ...
0
votes
1answer
75 views

WorkingPrecision and AccuracyGoal for using with NIntegrate

I'm modeling a quantum tunneling barrier. Because I want to express my quantities in mks units, that means that some of the variables I'm using are pretty small (10^-9). I use NIntegrate for part of ...
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
52 views

How to set Precision with a variable? [closed]

I get confusing output from the code below. If I put a number after a variable value, the precision gets set just fine. But if I put a variable after the backtick, MMa multiplies the values. Three ...
1
vote
2answers
61 views

Using a rule to increase precision [closed]

I'm sure this is a very simple question, but I can't work out how to do it. Construct a rule to set x=0.32 to a precision of 20 digits. The rule is to be applied ...
1
vote
1answer
79 views

NIntegrate discrepancies

I want to compute a numerical integral for a gaussian trivariate distribution. Say ...
6
votes
0answers
131 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: ...
0
votes
1answer
110 views

Precision of Eigensystem? [closed]

I was using Eigensystem to obtain the rotation matrix. However, I find out Mathematica does not fully diagonalize my matrix (or say not precise enough). My matrix ...
3
votes
1answer
64 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: ...
0
votes
0answers
22 views

N[variable,2] displays 6 digits [duplicate]

The following code doesn't behave as I expect. Rather than getting 2 digits upon varying r, I get the default value of 6 digits. What's up? ...
2
votes
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. ...
6
votes
1answer
151 views

Bug in ListPlot?

I want to check if this is a bug before I email WR about it. I can't get ListPlot[] to make scatter plots over a very small area: ...
4
votes
1answer
149 views

A difficult precision problem

I need to calculate values of a highly nonlinear recursive function, and I am confused by the results Mathematica is returning. ...
0
votes
1answer
63 views
0
votes
0answers
41 views

Maintaining working precision in my program

I am badly stuck with this program I am writing. I want output of program below to be precise up to 25 digits after decimal point. I am supplying all inputs with precision 25. But after each iteration ...
0
votes
0answers
30 views

How to fill in missing points on a graph? [duplicate]

If I plot the function Plot[Surd[x, 10], {x, 0, 10}, PlotRange -> {{-3, 3}, {-2, 2}}] I get This issue I have is that graph does not extend down to the ...
1
vote
1answer
110 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? ...
2
votes
2answers
115 views

How can I increase the precision of my table?

I want to see first 15 digits for the values in the table computed below. ...
7
votes
1answer
83 views

Change system options in package

I use Mathematica mostly for numerical calculations, and sometimes the performance of numerical calculations can be greatly improved if the high-precision arithmetic can be switched off by ...
0
votes
2answers
81 views

Exact calculating the multiply of two real [closed]

As the machine calculate,the exact calculating with real number have some problem to puzzle me long time.We know the 0.142*0.36523=0.05186266 is exactly equalized ...
1
vote
1answer
105 views

Wrong root when using numerical values

I have the following inequality: $$ \sqrt{\frac{a}{2x}}+ \frac{b}{1-\frac{a}{a+\sqrt{a(2bx + a)}}} + \frac{a}{2x\frac{a}{a+\sqrt{a(2bx + a)}}\left(1-\frac{a}{a+\sqrt{a(2bx + a)}}\right)} < f $$ on ...
0
votes
1answer
53 views

Why won't something print with desired precision in a while loop?

I have a problem: when I ask something to print with precision P, that is, Print[N[something, P]], it does not print with precision P, just with the usual output precision. In particular, I have a ...