Questions tagged [precision-and-accuracy]
The precision-and-accuracy tag has no usage guidance.
529
questions
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13 views
Shouldn't NIntegrate return a number whose precision is PrecisionGoal, not WorkingPrecision?
I know that Mathematica has great built-in precision tracking, so when you do calculations with arbitrary-precision numbers, Mathematica keeps track of the precision on the result. Given this careful ...
3
votes
3answers
134 views
How to convert a real number to a string only in the original length?
Example: I have this number
num = 2.9525730420542016*10^1798
(* 2.952573042054202*10^1798 *)
If I want to convert it to a string, I don't get "2....
3
votes
1answer
46 views
Rationalizing only specific terms in an expression
How can I change an expression like
A = (-1. a)/(x + y) - (2.1 b)/(x + y) + 4.1 + 2. x + (3. r s)/(x + y)
so that -1. a becomes ...
2
votes
1answer
46 views
Problem with the precision while plotting a figure
I am trying to plot eigenvalues of a 16x16 matrix.
Below you can see the code. I get some errors like “precision may be lost”, and “Eigenvalues at some positions are expected to be the same”.
As a ...
1
vote
2answers
62 views
Accuracy of Mod[x, 1] and FractionalPart[x]
The difference between exact and numerical computation is clear to me. But why is
...
8
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2answers
236 views
Computing separatrix orbit
I would like to numerically compute the separatrix orbit for a particle in a few potential wells, given by the negative of
...
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0answers
26 views
How to avoid machine underflow for plotting and integrating?
I am trying to integrate the following integrand, which I have plotted:
...
1
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1answer
68 views
Lowest Eigenvalue of a large sparse matrix without choking up the RAM (Corrected) [closed]
I am trying to find the lowest eigenvalue of a large sparse matrix of dimension N (=$3^n$, where n is number of particles in system ) using ...
2
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4answers
199 views
1
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1answer
36 views
Problem with label and precision
I need to define a function that depends on a variable taking values on discrete values, for example:
...
2
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1answer
148 views
(Numerical) calculation of nested integrals
The problem
I'd like to (numerically) compute nested integrals of the type $$I(a;k) \equiv \left( \prod_{i=1}^k \int_0^\infty \mathrm{d}x_i \right) \exp \left( - \frac{1}{4a} \sum_{i=1}^k \left( x_i - ...
3
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0answers
42 views
Behavior of $MinPrecision seems to have changed between 12.0.0 and 12.1.1
I am running into a very weird bug where setting $MinPrecision to some value (in this case 200) has a very different and ...
1
vote
1answer
89 views
Exported Excel File - decimals
Im trying to export data from the interpolating function result to excel.
everything works fine and the plots are as expected, but if I want to export these data to excel using
...
3
votes
2answers
93 views
Why is DistributeDefinitions taking so long with 100-300 Mb constants?
Why does DistributeDefinitions take so long to distribute variables that are 100-300 Mb in size?
I am setting up ParallelTable ...
0
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2answers
140 views
Can someone please comment on the efficiency of Mathematica, Maple and Matlab in conditional plotting?
I use Mathematica to plot
...
1
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2answers
66 views
How to make sure that the number of PlotPoints is sufficient for giving the complete result? (How to have a plot of the whole solutions?))
I want to see the domain in which function $f$ is positive. I use this code
...
0
votes
1answer
61 views
Why is this integral throwing a “MemoryAllocationFailure” error?
The following call to NIntegrate throws the error:
Throw::sysexc: Uncaught SystemException returned to top level. Can be caught with Catch[[Ellipsis], ...
5
votes
2answers
123 views
Wish to compute ln(x) with millions of digits of precision fast as possible
Computing $\ln(10)$ to 6 million digits of precision on my 2.5 GHz machine running Mathematica 12.1 takes about 23 seconds using the methods below. Wish to compute $\ln(x)$ with much higher precision....
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0answers
24 views
FindRoot does not satisfy PrecisionGoal but gives no error message
I use FindRoot to find a root to the equation
...
0
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1answer
40 views
$MaxPrecision doesn't work
I want to set MaxPrecision low, to like 2 decimals, but after I set it, it stays at 5 regardless.
I've tried using two commands:
...
1
vote
1answer
57 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
38 views
How to improve the accuracy of the data involved in the calculation?
I want to draw the error of the two iterative methods.
...
asked Oct 2 '20 at 0:10
A little mouse on the pampas
4,4402 gold badges9 silver badges27 bronze badges
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0answers
30 views
Improve numerical integration precision for multi-dimensional Integral
I have the following 4-dimensional integral
...
0
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0answers
59 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 ...
7
votes
4answers
314 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
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2answers
60 views
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2answers
36 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
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1answer
74 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
138 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
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0answers
36 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
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0answers
32 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
80 views
0
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1answer
55 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
39 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
104 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.
$$\frac{1}{16} \left(\sinh (\pi x) \left(64 \left(x^2-4\right) \cosh \left(\frac{2 \pi x}{3}\right) \cos (y)+\left(x^2+4\right)^2+256 x \sinh ...
3
votes
0answers
126 views
Discrepancy between the results of NIntegrate with different methods and options
I am trying to perform a numerical integration on a function defined through a sum of exponential terms. The summation is given by:
...
1
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1answer
68 views
Can not get n-digits precision with N[expr, n] in WSTP
I am new to Wolfram Language and wolfram engine. I use wolfram engine development kit to increase the precision of the output from Spherical Bessel function from WSTP in c++. Part of codes that ...
4
votes
1answer
124 views
What is the most accurate way of getting the highest derivative from NDSolve?
I would like to compare my simulations in Mathematica to measured data. I measure acceleration but for simulations the starting point is displacement. How does one get accurate simulations of higher ...
2
votes
1answer
79 views
Two different results for the same differential equation while using “AccuracyGoal”, “WorkingPrecision” and “PrecisionGoal”
I saw some strange behavior as I was solving a differential equation, so I decided to plot the solution in three different conditions.
First, I defined the initial conditions and some constants:
...
7
votes
2answers
325 views
Is it possible to do this two-dimensional numerical integration more precisely?
I am considering the following integral:
$$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
119 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
36 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
44 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
106 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
105 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
65 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
85 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
99 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 ...
