**273 precision questions.**

I'm trying to use regionplot for functions that involve Erfc. A slightly contrived example follows, but it illustrates my difficulties. The command
...

I'm trying to solve nonlinear equations using Newton-type methods with very high accuracy using Mathematica. I found many research papers in which the numerical results are calculated with very high ...

First of all, apologies for the large numbers, I couldn't find a working example for a far lower order and the zeros are necessary...
my problem is this:
I have a large polynomial (from high-order ...

Task
I am trying to evaluate the contour integral of some functions. To have a concrete example, let's use
$$ f(z,s) = \frac{1+(4+2s)\, z}{z - \left( 9 + 35s + 24s^2 + 4s^3 \right) z^2 + 8z^3} $$<...

I am a new user in Wolfram language.
Please, I am trying to calculate accurate solutions $R$ of an algébric equation which contains the Dawson function. The equation is:
$$1+\frac{\theta }{k^2}+\...

I need to find a way to set a global precision for my script in Mathematica. I want all results to be given with only 2 decimal digits. I already check the questions/answers from Setting precision ...

My code requires to set some precision to get more accurate results. But I found when I set the precision like 20 or 30, the computation speed would jump 7-10 times slower...
Here's an example:<...

I want to define a nice function Φ in 3D that is computed as follows
$$
\phi (x, y, z) = - z + \frac{\sqrt{32}}{\pi} \sqrt{\cosh \nu - \cos u} \sum_{n = 1}^\infty ...

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 ...

I have high precision data that I want to do Fourier transform with, but it looks like the precision is lost dramatically.
...

I just want to get a smooth plot but the calculated values are "discrete" which seems to be a precision problem. I tried N[],SetPrecision[],SetAccuary[] without any success. So I paste the Code in its ...

Recently the decimal expansion of a number theoretic constant
was searched for, which is the analog of the Landau-Ramanujan
constant in a certain context. The constant starts 0.638909...
It can be ...

I would like to print out an list of reals in a table with perfectly identical number of digits so that they can be perfectly right-aligned. However, once I convert them to strings, ...

I can't see the small changes of my function when I plot it. What can I do?
...

I am solving PDE by means of NDSolve and I am interested in a highly accurate value for the solution at a certain point. For some reason, the solution obtained by ...

I need to solve an ODE with very high precision. I am not sure yet how much precision I need so I have some question before changing the settings.
From what I understand, the working precision is how ...

I am trying to evaluate sums involving LegendreQ[n,x], the n-th order Legendre function of the second kind $Q_n(x)$, at large $x>1$. However, the problem is that ...

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 ...

When I do something a little bit more complicated than standard documentation examples, I often hit precision problem.
Or I accidentally disprove Riemann hypothesis Like this
...

EDIT: I filed a bug report and after a small back-and-forth the support person agreed this is a bug. He said: "I have filed a report with the developers to issue warning messages when the arithmetic ...

I found this and this on this StackExchange as to why Mathematica rounds half to even, which means thatRound[{0.5, 1.5, 2.5, 3.5, 4.5}]gives
...

I have the following codes. Naturally, I expect to get zero. I thought it is due to some possible issues stated as "Machine-precision inputs can give numerically wrong answers on branch cuts:".
...

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-...

I have an array a with 9 components and when i set precision for this array, components of a also get the precision.however, i want to avoid that and only the number get the precision. for instance, a[...

This is a problem confusing me for years.AccuracyGoal and PrecisionGoal are two options that I never truly understand and, to ...

I use Mathematica mostly for numerical simulation, so most of the time double precision (or machine precision) is enough for me. Mathematica has this nice feature of automatically upgrade to arbitrary ...

I am trying to wrap my head around floating-point precision. Performing the following numeric operation:275./6.*1.03692775514337in Mathematica and C++ and ...

I was looking in Mathematicas documentation and could not find to which point Mathematica includes the IEEE 754 standard?
It is mention it in its documentation MachinePrecision under Background & ...

I have this codep = Predict[{1 -> 123456789123456789, 3 -> 987654321987654321}]values are big, more than 15 digits (standard machine precision).
when I ...

Suppose I want to numerically evaluate an integral of the form
$$\int_{-\infty} ^\infty f(x) \mathrm{d}x $$
with error not exceeding some positive bound $\epsilon$. Is there a way to do this using <...

I have a function f(x) which I would like to see going up for very low values of x: from an asymptotic study, I expect it to go to Infinity for low x; however, I can see an elbow and many oscillations....

This Mathematica tutorial notes some strange behaviour with calculations such as Sin[10^50]:
...

I have data imported from excel file into mathematica but mathematica automatically converts large number into scientific form and when transferring this data to sql string field i get the following .....

I've been suggested (https://stats.stackexchange.com/questions/314930/what-is-a-reasonable-alternative-when-the-mean-does-not-exist) to use TrimmedMean to calculate ...

I have a list of functions that I want to apply to a same argument. What I did is something like{f[x],g[x],h[x]}/. x->N[10^6,300]One of the functions is <...

I want to understand how small numerical errors propagate through a computation and may drastically change the final result.
To this end, I consider a toy world in which every number is limited to ...

Hi I'm working on some numerical integration that needs to be evaluated up to a certain number of digits, however, I encounter the following problem:
If I use,
...

I'm trying to integrate a bunch of expressions similar to
...

I want to change the precision of a $3\times8400\times3072\times2$ matrix to 25, it's original precision is 5. Here is my code:
...

I have solved a set of 6 differential equations with DSolve. When I use the table command and produce the results of one of the equations given by DSolve, the ListLinePlot command gives me the correct ...

I'm trying to solve the problem of heat conduction through soil with periodic temperature variations on the surface.
For now I'm working with a 1D model but I see that the solution doesn't work, it ...

In order to speed up the memoization of data generated via NIntegrate, a possible approach is to use Compile on both NIntegrate function and the function itself separately. How can one set the ...

I've been reading the documentation in Mathematica about precision, namely:
Exact and Approximate Results
Arbitrary-Precision Numbers
Arbitrary-Precision Calculations
Machine-Precision Numbers
...

I am solving a differential equation:
...

I have been developing a Manipulate plot to put on the web. One of my parameters varies over a small interval, ...

I am solving my problem with LinearProgramming. In certain cases, my coefficients that are fed into the function come from evaluating trigonometric functions, $\sin(...

Since the precision is very important in my case, I am curious how precise is the MMA result for this integral:
...

I'm trying to plot a set of points, Mathematica create the plot with the right range but it doesn't show all the digits (only shows up to six digits):
...

I have an integrand that looks like this:
the details of computation are complicated but I only know the integrand numerically (I use NDSolve to solve second order ...

- numerics
- accuracy
- numerical-integration
- machine-precision
- plotting
- arbitrary-precision
- special-functions
- equation-solving
- differential-equations
- error
- matrix
- linear-algebra
- mathematical-optimization
- number-representation
- numerical-value
- output-formatting
- complex
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- summation
- list-manipulation
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