Questions tagged [precision-and-accuracy]
The precision-and-accuracy tag has no usage guidance.
509
questions
1
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1answer
43 views
Export high precision data to HDF5
Recently, I would like to use HDF5 instead of CSV because of times Import taking.
Especially, I have to manage large data with high precision (about 50 degits) and ...
1
vote
1answer
37 views
How to improve the accuracy of the data involved in the calculation?
I want to draw the error of the two iterative methods.
...
0
votes
0answers
28 views
Improve numerical integration precision for multi-dimensional Integral
I have the following 4-dimensional integral
...
0
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0answers
49 views
Significant digits
I have a rather silly question, so please excuse me=)
Let's say I have a general Mathematica code, where I numerically evaluate and combine several quantities. I would like to know how to determine ...
6
votes
2answers
232 views
Why do isolated large values of WorkingPrecision fail in NDSolve?
Executive Summary:
Getting an accurate answer often depends on setting the WorkingPrecision high enough. Once it is high enough, though, I would expect that its ...
1
vote
2answers
58 views
1
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2answers
34 views
Expression evaluates to a different number when made a function
The following expression evaluates to zero at large n when just using replacement, but if the same expression is defined as a function ...
2
votes
1answer
68 views
Precision on FindRoot
I am trying to solve a non linear system of equation, and when I solve it, I have the following message
FindRoot::lstol: The line search decreased the step size to ...
1
vote
4answers
136 views
Can I change the default behavior so that “0.1” is interpreted as “1/10” automatically?
Consider the function
f[a_] := NIntegrate[Sqrt[a + Log[x]], {x, 1, 10}, WorkingPrecision -> 30].
With this definition, I cannot call ...
0
votes
0answers
34 views
Increase precision of ConvexHullMesh
I want to generate a set of equations for all planes in the convex hull as specified in this question. The problem is that the generated set of equations don't correctly cover all the points. I run a ...
1
vote
0answers
31 views
When do errors stop calculations? [closed]
When plotting Plot[Exp[-1/(1 - (x + 10)^2)], {x, -11, -10}], I get the following warning
but the Plot follows. However, if I ...
2
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2answers
76 views
0
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1answer
52 views
Is there an alternative way instead of increasing the number of plotpoints in RegionPlot to get a better result?
I have this function and I use RegionPlot to see in which part of the domain, the function is negative:
...
0
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0answers
36 views
Mathematica precision on extensive eigenvalues calculations
Im trying to evaluate some dot products with eigenvectors and matrices using Mathematica. My problem is the following:
To an given matrix 6x6:
...
0
votes
2answers
81 views
How can I make sure that the plot of this function cross each other or not?
I have this function:
$$\frac{1}{16} \left(\sinh (\pi x) \left(64 \left(x^2-4\right) \cosh \left(\frac{2 \pi x}{3}\right) \cos (y)+\left(x^2+4\right)^2+256 x \sinh \left(\frac{2 \pi x}{3}\right) \...
0
votes
2answers
93 views
Is it needed to increase the precision of ContourPlot in this case?
I have this function and I want to see where it is zero.
$$\frac{1}{16} \left(\sinh (\pi x) \left(64 \left(x^2-4\right) \cosh \left(\frac{2 \pi x}{3}\right) \cos (y)+\left(x^2+4\right)^2+256 x \sinh ...
3
votes
0answers
125 views
Discrepancy between the results of NIntegrate with different methods and options
I am trying to perform a numerical integration on a function defined through a sum of exponential terms. The summation is given by:
...
1
vote
1answer
52 views
Can not get n-digits precision with N[expr, n] in WSTP
I am new to Wolfram Language and wolfram engine. I use wolfram engine development kit to increase the precision of the output from Spherical Bessel function from WSTP in c++. Part of codes that ...
4
votes
1answer
110 views
What is the most accurate way of getting the highest derivative from NDSolve?
I would like to compare my simulations in Mathematica to measured data. I measure acceleration but for simulations the starting point is displacement. How does one get accurate simulations of higher ...
2
votes
1answer
72 views
Two different results for the same differential equation while using “AccuracyGoal”, “WorkingPrecision” and “PrecisionGoal”
I saw some strange behavior as I was solving a differential equation, so I decided to plot the solution in three different conditions.
First, I defined the initial conditions and some constants:
...
7
votes
2answers
316 views
Is it possible to do this two-dimensional numerical integration more precisely?
I am considering the following integral:
$$J(x_1^2, x_2^2) := \frac{3 \cdot 2^{15} \pi^4}{96} x_1^2 x_2^2 \int_{-\infty}^\infty d\tau_3 \int_{-\infty}^\infty d\tau_4 \int_{-\infty}^\infty d\tau_5 \...
1
vote
2answers
115 views
Does SetPrecision[x, Infinity] expose the internal exact number in the approximated number?
What I already know (maybe) :
My theory about Mathematica's way of implementing approximated number
An number approX with arbitrary precision ...
1
vote
1answer
34 views
Can I configure a guaranteed precision for NIntegrate on a monotone function?
I know there are some great posts already about why PrecisionGoal->n doesn't guarantee the result of NIntegrate will actually ...
0
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0answers
39 views
Help with NMinimize and setting limits
Im trying to minimize the error of a function Penality that i have defined and am using the following code.
...
3
votes
1answer
86 views
Why does precision decrease after increasing PrecisionGoal and WorkingPrecision on this integral?
I am trying to calculate a messy double-integral to many digits of precision. As shown below, the precision seems to increase reliably as WorkingPrecision goes from ...
0
votes
1answer
92 views
How to improve working precision?
I'm trying to fit the array data as follow:
NonlinearModelFit[
data,
s*t^r + (A/(w*(Pi/2)^0.5))*Exp[-2*((t - u)/w)^2],
{s, r, A, w, u},
t];
But when ...
0
votes
0answers
63 views
Numerical evaluation expression not returning result in requested precision
I have a long list of descriptive statistical quantities for a univariate list of data. The problem is that the set number of significant figures is ignored by the ...
2
votes
1answer
83 views
ListLinePlot works for data similar up to 9 decimal numbers but does not work when similarity is up to 11 decimal numbers. Why?
Through the following code, Tcvalues are generated:
...
4
votes
1answer
94 views
A pattern replacement to force Mathematica to replace inexact 0 multiplication by zero
Hi Consider the following expression which contains multiplication by inexact 0
...
2
votes
0answers
32 views
Setting the tolerance for `Equal[]` [duplicate]
I would like to control how Equal[] works and allow a certain error associated with it. I would like numerical values which are, say, within one-thousandth of one ...
2
votes
1answer
85 views
A probable misdescription of official Doc about $MachinePrecision?
According to the official documentation:
When you enter an approximate real number, the Wolfram Language has to decide whether to treat it as a machine number or an arbitrary‐precision number. Unless ...
-1
votes
1answer
87 views
About the Rationalize of an approximated number
In[3]:= Clear["*"];
approPi = N[Pi];
{Rationalize[approPi], Round[approPi, 10^-15]}
Out[2]= {3.14159, 3141592653589793/1000000000000000}
Above ...
0
votes
0answers
68 views
Precision[] and Accuracy[] give non-integer result
a = N[Pi, {20, 19}];
Precision[a] (*19.497149872694134`*)
Accuracy[a](*19.`*)
Accuracy[a]*Log2[10] (*63.116633802859894`*)
My question
The ...
0
votes
0answers
25 views
Can certain precision goals not be met by NIntegrate?
I am running into a problem with NIntegrate where PrecisionGoal cannot be met. An example is as follows:
...
0
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0answers
62 views
Understanding Working Precision - two example equations
I am trying to understand how WorkingPrecision works, and in general how very small/large numbers are to be handled.
Let me preface I probably do not have ...
1
vote
3answers
63 views
Loosen tolerances to get a solution from NSolve for trig system
This is more an exercise in learning Mathematica than a real issue because the solution for me is just to solve half of the system.
I have a simple system of trig equations and can't solve the angle, ...
0
votes
1answer
40 views
How to initialize arbitrary precision?
How do I calculate $$\frac{1}{{\frac{1}{7 \times 10^7}- \frac{8\times10^{17}\times 3.1\times 10^7}{6.7 \times 10^{-11}\times \left(1.9 \times 10^{27}\right)^2} }}\tag{1}$$
To arbitrary precision?
I ...
2
votes
1answer
36 views
Not getting requested numerical precision
I am trying to do some calculations of probability and have run into an issue where Mathematica won't give me the requested number of digits in the result.
...
2
votes
2answers
54 views
relative accuracy in FindRoot
In my code I have function which takes large value, e.g. y[x_]=10^15 (2 - x^2)
When I try to find a root for such function, ...
1
vote
0answers
49 views
Numerical precision - simulating an unstable equilibrium
I was playing around with NDSolve and the following ODE
s = NDSolve[{y''[x] == -Sin[y[x]], y[0] == \[Pi], y'[0] == 0 },
y, {x, 0, 120}]
The equation and the ...
1
vote
0answers
31 views
Problem with Set Precision [closed]
I am using Set Precision to calculate data point pairs (t,Y) in a table:
Table[{t, SetPrecision[test[t], 4]}, {t, 0, 135, 7}],
Works fine until I try to copy and paste the list into another list ...
0
votes
1answer
55 views
Precision in mathematica [closed]
I am having some trouble with mathematica, i need to precise calculations and he is rounding my numbers and taking decimal cases from them and i wanted to know if there's a way i can tell him to stop ...
1
vote
0answers
22 views
How to dynamically increase sampling rate for NIntegrate?
I am trying to numerically integrate a messy function over the range $(0,\infty)$. Rather than integrating to $\infty$, I programmed a dynamic cutoff for which I can specify a desired precision. For ...
2
votes
1answer
100 views
Question about accuracy of this improper integral calculation
I have an integral (where $q$ is a constant and $u\geq1$)
$$\boxed{I = \frac{e^{(-q/4)}}{2\sqrt{2\pi}q^{\frac32}}\int_{1}^{\infty}\bigg(\frac{u-1}{u+1}\bigg)\int_{u}^{\infty}\frac{xe^{-x^2/(4q)}}{\...
1
vote
1answer
83 views
Plot Arc Length Parametrization
I want to plot the parametrization of the curve with respect to arc length. It is all known that we have to find the inverse of the arc length of the original function i.e. $F(t)$, and ...
2
votes
0answers
42 views
Set Underflow precision in Mathematica 12 same as version 11.x [duplicate]
It seems like Mathematica version 12 sets arbitrary underflow precision depending on the function, but I would like the underflow precision to be same as what was for previous version of Mathematica ...
1
vote
0answers
54 views
FindRoot giving error in Mathematica version 12
I was using the same code in previous version of Mathematica but unfortunately I had to update Mathematica to version 12 because I upgraded MacOS to Catalina. Now when I run my code, I get this error
...
1
vote
2answers
83 views
How to convert a number with more decimal places to the number as it shows on the screen?
I came across a situation where many results got many decimal places. For further calculations in my situation, I would just take the value as it shows on the screen and drop further digits. For ...
1
vote
1answer
84 views
Adjusting PrecisionGoal and AccuracyGoal when solving my equation using NDSolve?
Thanks for paying attention to my question and modifying my terrible formatting[facepalm], now I think I've found the answer. The point is the selection ...
1
vote
2answers
112 views
