Questions tagged [precision-and-accuracy]
The precision-and-accuracy tag has no summary.
662 questions
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How to increase the precision and accuracy for computing eigenvectors of a large matrix NUMERICALLY?
I have a large 40*40-dimensional matrix $H$ and I need to find its eigenvalues and eigenvectors. The elements of the matrix are complicated, mostly in the form of Root[544 ... - 6790 #^39 + #^40& ...
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Plot of $x^{\epsilon}|\log{x}|$ near zero
Fix $\epsilon\in (0,1)$. It is an elementary fact of calculus that
$$\lim_{x\to 0^{+}} x^{\epsilon}|\log{x}|=0.$$
When I plot the function $x^{\epsilon}|\log{x}|$ using Mathematica 13.2 I see a blowup ...
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Integrating high order Legendre polynomials
The Legendre polynomials $P_\ell$ are defined for each $\ell\in\mathbb N_0$ and are given in Mathematica by LegendreP[l,x]. They are such that $|P_\ell(x)|\leq 1$ ...
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Fluctuating results with NIntegrate
I've been trying to calculate an integral using NIntegrate as follows.
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How to improve the accuracy of the coordinates generated by the GeometricScene and RandomInstance functions?
When using the GeometricScene function and RandomInstance function, I noticed that the coordinate precision appears insufficient ...
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The root neighborhood representation
I am trying to understand the content in the documentation for Root.
The root neighborhood representation Root[{f,c}] specifies ...
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How to improve and assess accuracy of NDSolve with a system of equations
I have asked about a single equation here and got useful advice. Now I am looking at a system of equations. At the moment the equations are linear, which is good for looking at accuracy, but I will be ...
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How do you increase the precision and accuracy of the numerical approximation of the Volchkov integral?
There is a need to increase the number of correct decimal digits from this integral:
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How to solve a regular integral with divergence analytically
I want to analytically integrate this integration
$$\int_0^{1 - 3/rs}\left(\frac{9 \sqrt{3} \sqrt{\frac{1}{\left(1-\frac{2}{\eta }\right) \eta ^2 \left(\frac{\eta
^2}{1-\frac{2}{\eta }}-27\right)}}}...
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Errors in solving a complex equation: FindRoot and NIntegrate cannot converge
I am trying to numerically solve a complex equation eq[x,y,μ] that includes a complex integral. The integrand contains the inverse hyperbolic tangent function ...
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Precision and Accuracy error in solving complex equation
Following @Bob Hanlon's suggestion in my previous post, I created the following Mathematica script for solving a new equation, more complicated than the previous one. The goal is to compute the ...
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How to change default precision for ALL variables and computations?
I struggled a lot to make a piece of code working. IN the end, it was all about changing all numbers to have high precision, for example I changed
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Strange results about the sine function of a big integer
I want to calculate the sine of a big integer, e.g., Sin[10^50], but found that N[Sin[10^50]], N[Sin[10^50],10], and N[Sin[10^50],20] give different results:
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