Questions tagged [precision-and-accuracy]
The precision-and-accuracy tag has no usage guidance.
576
questions
1
vote
1answer
63 views
Wrong limit appears [closed]
Consider the following limit
$$
\lim_{x\to-\infty}x-\sqrt{x^2+7x}
$$
Going through some algebra leads to
$$\begin{align}
\lim_{x\to-\infty}x-\sqrt{x^2+7x}&=\lim_{x\to-\infty}\frac{(x-\sqrt{x^2+7x})...
1
vote
0answers
43 views
Mathematica returns zero for small rational number to 1/133 power but not zero [closed]
This small number raised to the 1/133 root is not zero but Mathematica is underflowing with the computation. I assume Mathematica is first computing the quotient numerically, then taking the root:
<...
0
votes
1answer
52 views
Minimizing a quadratic form: Failed to converge to the requested accuracy or precision within 100 \ iterations
I'm trying to minimize this type of quadratic form:
...
1
vote
0answers
76 views
How to calculate precise higher derivatives of ParametricNDSolve solution
Higher Derivatives of NDSolve don't match the results from DSolve solution, can I somehow increase the accuracy of numerical method to match arbitrarily high derivatives?
Equation
I am using ...
0
votes
1answer
59 views
Issues with Nintegrate - different methods yielding different values (both giving warnings)
I am integrating the following function
\begin{equation}
\frac{1}{2d^{2}}\times\frac{\sqrt{\omega_{c}\left|t_1-t_2\right|}-\sqrt{\pi}e^{\frac{1}{\omega_{c}\left|t_1-t_2\right|}}\text{erfc}\left(\frac{...
0
votes
2answers
68 views
Same integral yielding to different results
I am currently working with the following integrals
\begin{equation}
\int_{0}^{\infty} dk\thinspace \frac{k^{3}e^{-2kd}}{\omega^{2}+k^{4}} = \frac{1}{\omega^{2}d^{4}}\int_{0}^{\infty}d\epsilon\...
1
vote
0answers
46 views
plot and limit are not in agreement [closed]
I am plotting the following function $\frac{\sqrt{t \text{$\omega_c $}}-\sqrt{\pi } e^{\frac{1}{t \text{$\omega_c $}}} \text{erfc}\left(\frac{1}{\sqrt{t \text{$\omega_c$}}}\right)}{(t \text{$\omega_c$}...
3
votes
1answer
49 views
About Numerical Precision Related with Zeros [duplicate]
I encounted the following precision issue. I define c = a + b, but the result for 'c - a - b' does not equal zero. I am not sure how to resolve this.
'''
...
2
votes
2answers
190 views
How can I make sure that there are real roots for the given function? Can I trust the plot only?
I have this function
$$f(x)=(\pi -2 x)^2 \sin \left(\frac{\pi ^2}{2 x-2 \pi }+\frac{1}{2} \csc ^{-1}\left(\frac{4 \pi (\pi -x) \csc \left(\frac{\pi ^2}{x-\pi }\right)}{4 (\pi -x)^2+\pi ^2}\right)\...
0
votes
1answer
34 views
0
votes
1answer
59 views
Precision problem with mathematica
I have a precision problem with a complicated function in Mathematica. I need to get norm (NIntegrate[f[x],{x,0,1}]) and shape (...
0
votes
1answer
24 views
SetPrecision with Manipulate using variable number of controls
I want to convert inputs from controls in Manipulate into exact numbers and have two kinds of inputs:
parameters: there are a fixed number of these
rates: the number of rates is controlled by the ...
0
votes
0answers
60 views
Mathematica accuracy errors when creating data
I created training data for a neural network and below are two errors I got
The only code that uses "FindRoot" command is the following
...
0
votes
1answer
57 views
General:munfl error problem
I have the following function, that is the result of The integration between x and some upper limit of a positive function, thus should be positive
$f(x,vE) = \frac{e^{-1140.09 x} \left(e^{67945.5 \...
1
vote
0answers
33 views
How does WorkingPrecision in NDSolve handle MachinePrecision?
I'm wondering why the following code
NDSolve[{y''[t] + y[t] == 0, y[0] == 1., y'[0] == 0}, y, {t, 0, 10},
WorkingPrecision -> 6]
throws the error/warning, that ...
0
votes
1answer
100 views
DiscreteMarkovProcess: preparing the transition matrix and unexpected negative results
I would like to implement a Markov process.
It consists on a walk on a one-dimensional lattice, with nodes spaced $\epsilon$ from $-2$ to $2$.
The transition probabilities for $x \neq y$ are as ...
2
votes
1answer
92 views
How do I force mathematica to output more digits for this particular expression? [closed]
I'm working on a project where a certain calculation of $\pi$ to an arbitrary precision is required. I'm evaluating the below expression in Mathematica:
$6\sum_{k=0}^{\infty}\left(\frac{\left(-0.5\...
0
votes
0answers
16 views
Why increasing PrecisionGoal and WorkingPrecision is deteriorating my results
I am minimizing a variable subject to many very complicated constraints, like
...
0
votes
0answers
29 views
General::munfl - Precision lost in LinearModelFit
I am new to mathematica so I am confused regarding the loss of precision in LinearModelFit. In building a linear model with uora (1 or 2) and encodeSeverity (1,2 or 3)
...
3
votes
0answers
53 views
How to deal with too small numbers
When dealing with a code that produces too small numbers (in a complicated way) like
0.33691 4.015757066049965*10^-330
I get the following warning
General::munfl: ...
5
votes
1answer
121 views
Accurately computing $\sum_{j=2}^\infty \frac{(-x)^j}{j!} \zeta(j)$
I'm doing a sanity check of the following equation:
$$\sum_{j=2}^\infty \frac{(-x)^j}{j!}\zeta(j) \approx x(\log x + 2 \gamma -1)$$
Naive comparison of the two shows a bad match but I suspect one of ...
0
votes
0answers
35 views
Solving a determinant to get non-zero roots in a heat transfer problem
I am trying to solve a mathematical model of a heat transfer problem.
As an intermediate step there is a characteristic equation in the form of a determinant, which needs to be solved for variable <...
0
votes
0answers
41 views
How do I increase an amount of digits after the point?
I have an expression such as:
Log[0.784637, 517.8796]*ArcTan[-1.112673]*0.4256^(-2.034)*Sqrt[3.567]
and I get 3 digits precision. I tried:
...
2
votes
1answer
46 views
N::meprec warning when setting precision
How come
N[ Log[ Cos[1]^2 + Sin[1]^2 ] ]
evaluates to 0. without any trouble, while
...
5
votes
1answer
193 views
Airy function zeros, conflict (error?) between Wolfram Functions vs. Mathematica
According to functions.wolfram.com, the zeros of the Airy function $\operatorname{Ai}(z)$ occur at $z_k=f\left(\tfrac{3\pi}{8}(4k-1)\right)$ for $k\in \mathbb{N}$ where
$f(d)=-d^{2/3} \left(1 + \frac{...
1
vote
2answers
42 views
Compile generates non-tensor object warning for this simple function
Compile generates the following error (CompiledFunction::cflist: Nontensor object generated; proceeding with uncompiled evaluation.) upon execution of this simple ...
2
votes
1answer
98 views
NIntegrate fails to solve a double oscillatory integral
I need to compute the following integral:
...
1
vote
1answer
64 views
Removing artifact in Plot[1-(1-x)^Floor[2/x],{x,0,1/20}]
The input
Plot[1-(1-x)^Floor[2/x],{x,0,1/20}]
yields
where the white space we see below the curve near $x=0.01$ is an artifact. How can we fix this simply? ...
1
vote
0answers
40 views
Why does this reduce evaluate with exact numbers but not numbers specified to 20/50/200 decimals of precision?
Consider the following lines of code:
...
1
vote
2answers
74 views
Function decomposition to Fourier series using first impulse function
I have periodic function with certain first impulse function and period value. My task is to decompose it to approximate Fourier series (k_max = 10) using Laplace transform of first impulse function:
...
1
vote
0answers
48 views
Why don't AccountingForm, NumberForm and DecimalForm print more decimals?
I have the following set of equations:
...
0
votes
0answers
14 views
Setting precision of a result for the next calculation
Sorry for my easy question.
I would like to learn how I could change the precision of a value to use it for the next calculation ?
Lets say, a=9.96329x10^-13, in fact this value is so small and can be ...
0
votes
2answers
46 views
Confused by results of a simple computation [duplicate]
If I define
f[x_] := (1 - Exp[-2 x^2])/(x Sin[x])
and then enter
N[f[10^-5] - 2, 100]
I get the result
$$-1....
0
votes
1answer
51 views
The value of the function with a very small Imaginary part but can be Plotted
I have a function Y[x_,β2_], It can be plotted normally. But when I take specific values, I get something like +0.000000*I when ...
4
votes
2answers
177 views
Slider changes Pi to a MachinePrecision number
Problem
Consider the following code:
DynamicModule[{a = {0, Pi}, b = 4},
{Slider[Dynamic@b, {a}], Dynamic@b}
]
I want a Slider...
0
votes
1answer
99 views
Accurate Numerical values of a given functional
Consider the following functional :
$$
I(x,s) =\int_0^\infty\mathrm dy \frac{F(x + \mathrm iy, s) − F(x −\mathrm iy, s)}{\mathrm e^{2πy}-1},
$$
where $ F(z, s) = \dfrac{\sin^2[π\Gamma(z)/(2z)]}{z^s} $....
0
votes
0answers
36 views
How to copy and paste numbers with "`" mark and use them in calculations, without using N or setting precision every time
Suppose we have run a calculation and get a number like
2.758952615889003`
If we then copy-paste this number and do a calculation like
...
2
votes
1answer
22 views
1
vote
2answers
96 views
How do you overcome recursion limits when using DSolve?
I have the following program to solve for the neutron to baryon ratio during BBN. I've replaced many of the derived values with constants in order to focus on the problem:
...
0
votes
0answers
47 views
3
votes
0answers
74 views
0
votes
2answers
61 views
Precision in Integrals and NDSolve
I have a simplest code for NDSolve, the problem is I am dividing two small numbers, the denominator is so small that it gives me infinity as an answer, how can I increase the precision to get a ...
22
votes
3answers
9k views
5
votes
1answer
95 views
Find the number of correct digits to compare approximation with exact value
A) For simple example suppose i want to approximate $\pi$ using $\frac{22}{7}$ and $\frac{355}{113}$.
...
1
vote
2answers
128 views
Why can't Mathematica express a minus operation between two decimal numbers with several places? [closed]
A example of the problem. This is a print from mathematica with the demonstration of the issue.
3
votes
1answer
47 views
How to set Working Precision/ Accuracy global for the entire notebook in mathematica
F1[r]=((37.3042 - r) (-25.578 + r) (62.8822 + r))/(3000 r)
FindMaximum[F1[r], r]
The output is {0.0345106, {r -> 31.0723}}.
...
1
vote
1answer
46 views
10
votes
1answer
108 views
How to control floating point precision when `Export`ing to obj format?
Suppose we have a MeshRegion that we want to export to an obj file with, say double precision. Is that possible with Export? And ...
0
votes
2answers
42 views
How to export InputForm of a number
I need to export full form of a number i.e. the actual form with which Mathematica works. For example, full form of a number is
...
0
votes
0answers
92 views
Why can't NDSolve(Value) solve Maxwell eq. for plane wave i.c.'s when going to spherical coordinates (it works fine in Cartesian coordinates)
I would like to use NDSolveValue (or NDSOlve) to solve a set of PDEs in spherical coordinates. I started with a simplified example that resembles the problem I actually want to study, but where I know ...
