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Questions tagged [precision-and-accuracy]

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Find directional accuracy for combined forecast of ARIMA model and GARCH model

I want to use the below equation in the following forecast code. ...
VishnuPrasad 's user avatar
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1 answer
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Precision perplexity: how to get all the decimal places to show up [duplicate]

If I want to see 50 digits of precision, I turn to the N function: Like N[2/3, 50 gives me ...
dreeves's user avatar
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Getting better answers by smaller working precision?

I have the following code ...
Dotman's user avatar
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1 vote
2 answers
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Arbitrary precision workflow

Please, consider the following MWE representing my code: ...
fales's user avatar
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ContourPlot does not draw intersection point and draws ragged plots [closed]

I have the following implicit equation: $$ M^{-2\frac{\gamma-1}{\gamma+1}}(r)+\frac{\gamma-1}{2}M^{\frac{4}{\gamma+1}}(r) = \frac{g(r)}{g_0}\left( M_0^{-2\frac{\gamma-1}{\gamma+1}}+\frac{\gamma-1}{2}...
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Making NSum faster with higher precision and accuracy

I have the following code that I want to run to obtain a cumulative list out of various values of s1=3 to s1=10 (say) for the ...
QFTheorist's user avatar
4 votes
1 answer
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NIntegrate returns TerminatedEvaluation["RecursionLimit"] when called in another function

I try to perform some numerical integration with high precision on version In[1]:= $Version Out[1]= "13.3.1 for Linux x86 (64-bit) (July 24, 2023)" Here ...
SimonM's user avatar
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2 votes
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SetPrecision, SetAccuracy and how to guarantee $n$-digits are correct

Here are some things I believe are correct reading the documentation: If I do N[someArithmetics,{Infinity, 20}] I am guaranteed that the computation done (...
Confuse-ray30's user avatar
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Interpreter fails to obey significant figure specifications

Consider the following example, where we specify the precision of the numbers to perform a significant figures calculation: ...
Joshua Schrier's user avatar
1 vote
2 answers
339 views

Solving numerical equation with FindRoot with high precision

I try to solve numerically an algebraic equation wich contains Dawson's function. Solutions x of this equation depend on the two parameters a and b. Then I try to plot x versus a for a given b. Here ...
Gallagher's user avatar
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6 votes
3 answers
833 views

A bug with high precision

Consider the following two numbers: num1=0.0006000000000000001`; num2=0.0006000000000000003`; num2 appeared from ...
John Taylor's user avatar
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3 votes
1 answer
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How can I improve the accuracy of FindRoot for a complex equation?

I want to solve the following problem: Given a complex matrix $m=\textbf{m}(λ, ω)$, with $λ, ω \in \mathbb R$, find $λ$ and $ω$ such that $$\det[\textbf{m} (λ, ω)] = 0$$ Since one can take the real ...
fritess's user avatar
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How to refine ContourPlot3D result?

From this interesting question How to plot a surface given implicitly by 3 equations in 5 coordinate variables? I have found a subproblem that I would like to clarify: Often it is advantageous to use ...
Ulrich Neumann's user avatar
2 votes
0 answers
135 views

Is this result for the leading digits of $2^{2^{2^{32}}}$ accurate?

I have used Mathematica to compute the leading digits of very large powers. My largest calculation was to find the first digits of $2^{2^{2^{32}}}$, whose number of digits is itself a number of over a ...
Allam A.'s user avatar
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4 votes
2 answers
243 views

How to transfer a numerical value in Mathematica into a symbolic fraction with sufficiently large precision?

Suppose I have a number $0.26630939883535015$ and want to transfer it into a symbolic fraction by truncating it first. The way I do it is first Round it and then <...
narip's user avatar
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1 answer
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Calculating and plotting very small values gives errors

I want to plot the difference between $sin(x)$ and its Maclaurin series of order $200$ and more on $[0,1]$. When I run the code ...
Mohamed Mostafa's user avatar
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109 views

How to set the precision for the entire notebook

I want to do various computations conditional on a given precision for the entire notebook. I use the following code: ...
Tugrul Temel's user avatar
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1 answer
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Evaluation gives different results before and after simplifying expression

I am trying to evaluate $h(z)=\frac{f(z)}{g(z)}$ at points $z$ close to 0. Here I have taken an example value of $z=\texttt{z1}=10^{-7}$ for demonstration. I notice that evaluating the fraction before ...
sai's user avatar
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2 answers
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Generating sequence from a number with Precision

This question was from the End-Semester question paper of the previous year of my Course on Wolfram Mathematica - Apparently when I try to code it, something is going wrong with respect to Precision - ...
Venkatakrishnan's user avatar
1 vote
1 answer
64 views

Appying Function To All Elements Of A Long List vs Over List's First Element Gives Different Results

So, I have two lists, and a function. If I apply my function to both lists in a "listable" manner, I have one result, but if I apply it to lists' elements one-by-one, in a "map" ...
Anton's user avatar
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1 answer
116 views

Precision error in ND package

Based on the helpful answers to this question, I wrote the code below to compute zeros of the derivative of the Riemann zeta function, high in the critical strip ...
stopple's user avatar
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How to treat small numbers in order to gain efficiency and precision in neural network algorithm?

Unfortunately I won't be able to provide a MWE, as it would be too big and complex, and this question will be based on pure semantics, basically (and I understand if this is impossible to answer in ...
GaloisFan's user avatar
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1 answer
106 views

NMinimize can not find points that satisfy constraints

NMinimize cant find solutions for a function which clearly has one. Setting a working precision resulted in some output, however with error messages about tolerance and precision. Heres my code. The ...
Dotman's user avatar
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4 votes
0 answers
71 views

Orthonormal Wavelet functions

The wavelet function "WaveletPsi" is supposed to create an orthonormal basis of some space. Now consider e.g. the following wavelet function: ...
Daniel Huber's user avatar
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2 votes
1 answer
51 views

Spurious solutions when using NSolve on a simplified equation

I am solving an equation that should have only one solution in $[0,1]$, and as shown below, equ2 is a simplified version of equ1 ...
Lomath's user avatar
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Accuracy or precision issues with this code

I'm experiencing issues with the code below (this working code solves the Tolman-Oppenheimer-Volkoff (TOV) equations in general relativity, for the hydrostatic equilibrium of a spherical star). ...
Cham's user avatar
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0 votes
1 answer
110 views

Exp[-690255.2204176334] is too small to represent as a normalized machine number; precision may be lost [closed]

I'm trying to visualize the relationship of maximum temperature $(T_{m})$ with the heating rate with Randall-Wilkins theory for an energy depth of 0.85 eV. The Randall-Wilkins expression used is ...
D A.'s user avatar
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1 vote
1 answer
92 views

How to improve the accuracy of FindRoot or NDSolveValue at extreme conditions in my equation system?

This is a follow up question to my earlier one. I have posted a question related to a DAE system. Here is my earlier question and the equation system now I am asking for an answer is ...
Mikoto's user avatar
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0 answers
56 views

Overflow + Underflow Problems with Code

I am trying to use Mathematica to verify simulation results with an analytic result. The analytic results are performance measures of the M/D/1 queue, which unfortunately uses the factorial function ...
PiE's user avatar
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2 votes
3 answers
111 views

How to modify the given codes (NIntegrate of Boole) to get the most accurate result possible?

I have five conditions con1 to con5 over the two-dimensional domain $t,u\in[o,2\pi]$. I want to compute this area $(con1 \cap con2 )\cup(con3 \cap con4 \cap con5)$ numerically. I try the two codes ...
Martha97's user avatar
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1 vote
1 answer
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How to modify NIntegrate code below so that it gives the most accurate/reliable numerical result?

Imagine that I have two conditions con1 and con2 over the two-dimensional domain $x,y\in[-2,2]$. I want to compute the area of the union of these two conditions i.e. the region $(con1 )\cup(con2)$. I ...
Martha97's user avatar
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1 vote
1 answer
111 views

Higher precision with special functions [closed]

I'm currently working with the HeunB function, and am finding that its numerical precision is not sufficient at large arguments - in particular I have the function $\text{HeunB}\left[-k^2,1-\beta ,\...
Guy's user avatar
  • 285
3 votes
4 answers
472 views

Why is precision so low despite setting working precision to 25?

I am currently generating some Gauss-Jacobi quadrature rules. Along the way, I have to find zeroes of Jacobi polynomials. In particular, I have this piece of code: ...
Numerical Disintegration's user avatar
3 votes
2 answers
109 views

RegionFunction is imprecise

I've managed to print clipping a figure inside another. That's impossible out of controlling directly their coordinates (x, y[, z]), and then it's impossible to do a graphic clipping over an already ...
juanfal's user avatar
  • 31
0 votes
0 answers
43 views

Random precision in the digits

I am running Mathematica 12.3.1.0 under Windows 11 64-bit. Everything was running perfectly under Windows 10, until I updated to Windows 11. Now, I type, for example, k = 1.3807 10^-23 m = 1.3804 10^-...
Jose Luis's user avatar
1 vote
2 answers
177 views

WhenEvent in NDSolve -management of accuracy

I am bouncing a particle off various surfaces and using WhenEvent to determine when I hit the surface. Here are some very simple examples for when things go ...
Hugh's user avatar
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1 vote
1 answer
112 views

How to solve the problem with the error in FindRoot for non-linear equation?

Whoever is reading this have to be patient as the code is slightly long and I have explain each section in order to explain the problem. So I want to solve the set of non-linear algebraic equation ...
sslucifer's user avatar
  • 541
2 votes
2 answers
149 views

How to get correct numerical result without lots of digit precisions?

I am wondering if it is possible to get the correct numerical result without computing with a lot of precisions in expressions. as a simple example suppose in the middle of some of my numerical code ...
ghadir jafari's user avatar
1 vote
1 answer
106 views

How to improve accuracy of the integration in the following case?

Consider the following function dsPrimakovdtnucleus: ...
John Taylor's user avatar
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0 votes
0 answers
38 views

FindRoot::nlnum and InterpolatingFunction::dprec problem

...
dark knight's user avatar
5 votes
1 answer
139 views

Incorrect answer zero where correct answer is very large (precision issue)

Define a function F as follows: F[α_, x_] = N[Exp[x/2] Abs[Gamma[α/2 + I x /(2 Pi)]]^2, 10]; It is a product of two terms. ...
Laplacian's user avatar
  • 1,053
0 votes
0 answers
67 views

Answer changes slightly when re-run

I am trying to resolve why I get slightly different answers when I re-run my notebook. Here is my full code: ...
LTB's user avatar
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6 votes
2 answers
259 views

How to ensure for a solution of `NDSolve` to be positive?

I'am trying to solve kinetic equation for test particles in the Maxwellian plasma. It is Vlasov equation appended with Landau integral of collisions. It is proven that solution of such an equation is ...
Igor Kotelnikov's user avatar
2 votes
1 answer
142 views

Increase precision of matrix multiplication [closed]

I am computing U.U......U.x, where x is a vector, U a square matrix and the product involves N times U, i.e., (U^N).x if you like. One way to do this is ...
Philipp Strasberg's user avatar
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0 answers
43 views

Numerical integration converging too slowly with Tanhyberbolic function

...
Tiku's user avatar
  • 51
2 votes
3 answers
156 views

Accuracy and precision control for a simple calculation [closed]

Consider a very simple calculation: $231 \times (2.54) ^ 3$, which is the number of cubic cm in a US gallon. On my phone app calculator I got the exact answer, which is $3785.411784$. On Mathematica, ...
user56489's user avatar
1 vote
1 answer
151 views

How do I speed up this numerical integration with Bessel functions? (Tried changing Working Precision and Integration Strategies)

I need to compute the function P[b] given as follows: ...
Dave's user avatar
  • 11
1 vote
1 answer
61 views

LinearOptimization and Accuracy

Surprised to encounter the following issue in handling Accuracy with LinearOptimization: ...
user46831's user avatar
  • 643
0 votes
1 answer
100 views

Is there any alternative for conditional plot that gives a more precise result in a shorter time?

I have the given function $Func$ and want to have a plot of those domains where $-3\leq Func\leq 3$ in precise details. I am using ...
Phys96's user avatar
  • 361
1 vote
0 answers
75 views

How to handle "too small to represent as a normalized machine number" when plotting a figure [duplicate]

I am trying to plot a figure by the following codes: Plot[(27 2^((-2 + a)/(-1 + a)) 5^(a/(-1 + a)) 7^(1/(1 - a)) a^2)/((-1 + a) (4 + 9 a)), {a, 1.001, 3}] ...
Ya He's user avatar
  • 160

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