# Questions tagged [accuracy]

For questions about characterizing or improving the accuracy of a computational method.

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### Numerical algorithms made stable by unums which are unstable on IEEE floats

For unums, there is good evidence (see figure 5) that accuracy is better than IEEE floats. (Note: I use the term "unum" broadly to refer to any of the various iterations and revisions to the ...
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1 vote
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### What is the rationale of second-order finite volume discretization?

When it comes to a second-order accurate finite volume discretization of Navier-Stokes equations, which one of the two following rationales is adopted? 1- Second-order accuracy is a direct consequence ...
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### How to find the optimum finite difference method for derivatives?

Related to: What are the negatives of using higher order finite diference schemes? Problem: I have some discrete data of a trajectory $x_t$ with errors $\delta x_t$ of a physical system sampled at ...
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### Automatic finite differences

Given numbers $x, y \in \mathbb{R}$ where $$\frac{|y-x|}{|x|}$$ is small, and code that implements the function $f$ with a sequence of arithmetic operations, I would like to compute to high accuracy ...
• 8,695
1 vote
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### Comparison between stability and accuracy of various Finite Difference schemes

I`m Analyzing the 1D convection equation (PDE) for stability, consistency, and accuracy. I know Both upwind schemes (explicit and implicit) show better stability with a higher number of waves for ...
117 views

### Accuracy gap for apparently stable solution

I was reasoning about the behaviour of the methods I'm using for my simulation and I noticed that, considering $h_s$ as the timestep over which I have unstable solutions and $h_a$ as the timestep ...
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### How can I avoid catastrophic cancellation?

I have the following formula that I need to rewrite in order to avoid catastrophic cancellation. $$y =\sqrt{\frac{1}{2}\left(1-\sqrt{1-x^{2}}\right)}$$ As $x$ becomes smaller, $\sqrt{1-x^{2}}$ ...
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### How to get a more accurate cancelation

I shall try to get to the point, so let me know if there is something left and you need more details. I am solving a couple of equations that are not coupled explicitly, but their corresponding ...
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### Order of Accuracy Measurements on 1D Advection Methods

I am trying to learn about basics of computational fluid dynamics, at the moment on the simple example of linear advection in 1D. I am am currently testing the theoretical predictions of the order of ...
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### Derivative of Whittaker-Shannon interpolant

Last time we looked at how to improve the accuracy of Whittaker-Shannon interpolation, where user njuffa demonstrated that judicious use of sin_pi could greatly ...
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### Training accuracy improves but test set accuracy remains the same

I have built an ANN model with 5 hidden layers and 100 nodes in each layer to solve a multilabel classification problem. After the first run, I get a training accuracy of ~66% and a test set accuracy ...
208 views

### Whittaker-Shannon interpolation: Accuracy dies with speedup; can it be fixed?

With a truncated Whitaker-Shannon series (cardinal series) $$f(t) = \sum_{j = 0}^{n-1} y_{j} \frac{\sin\left(\pi( \frac{t-t_0}{h} -j)\right)}{\pi\left(\frac{t-t_0}{h}-j\right)}$$ we can naively ...
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### Cost functions to judge time/memory/accuracy tradeoffs

I am working on an interesting algorithm: Its absolute error is exponential in a parameter $j \in \mathbb{N}$, and for a given $j$, I have complete freedom to choose between an $\mathcal{O}(1)$ time-...
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1 vote
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### Adam Bashforth 4 method: how to determine starting values and stil keep the the order of accuracy

I am using an Adam Bashforth 4 method to solve an IVP problem so I need other numerical method to estimate the first 3 values. I am very much interested in finding a way to estimate the first 3 values ...
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### Accurate and efficient computation of the inverse Langevin function

The Langevin function $\mathcal{L}(x) = \mathrm{coth}(x) - \frac{1}{x}$ occurs in computations related to elastomers and paramagnetic materials. It is easily computed accurately and with high ...
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### When writing a research article, how to deal with deviations from theoretical expectations due to numerical errors?

We research the aerodynamics of the vehicle. Usually, there exists turbulence, which will cause the time-varying measurement of the force. The unsteady flow field determines we could not get a ...
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239 views

### Is it possible to proof a-b+b = a for all double floating-point numbers?

I want to know whether the equation : a-b+b = a is always true for a, b belongs to double precision floating-point number and |a|>=|b|. If the equation is true, how can I proof it? If not, what ...
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