# Tagged Questions

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### Using kalman filter when samples don't have time index

Assume $X$ and $N$ are two sets of observations from two different normal distribution, where $X$ represents clean data and $N$ represents noise; and $A$ a projection matrix of a filter and the ...
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### Difference between l2 norm and L2 norm

What is the difference between the $l^2$ norm and the $L^2$ norm. I can not find a definitive reference. Wikipedia uses them interchangeably.
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### How to avoid the round-off errors in the larger calculations?

Now I need to sum up more than one thousands of terms and then make the four-dimmensional integral in my Fortran program. I found that there are some numerical errors. Can you give me some suggestions ...
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### Calculation of error

I have written a code in which I find the approximation of the solution of this elliptic problem. I calculated the error using the following part of code: http://pastebin.com/7b5mmuRW but I get the ...
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### How can one describe the accuracy of a Runge-Kutta method?

I am solving a nonlinear ODE with a regular singularity using MATLAB ODE45 or ODE113. I am wondering what precision and accuracy they have and what one can say about the numerical error. The idea ...
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### GSL linear algebra LU/determinant precision

I am working with symmetric matrices of order $n \times n$ where $n \leq 50$. The diagonal elements of my matrices are a fixed number $d$ and the off diagonal elements are limited to two small numbers ...
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### problem about simulating recurrence relation

We have the recurrence relation: $5x_{n+1}-x_n=\frac{1}{3}$ $x_0=\frac{1}{12}$ solution: $y_h=(\frac{1}{5})^nC$ $y_p: 5A-A=\frac{1}{3}$ $A=\frac{1}{12}$ $y=(\frac{1}{5})^nC+\frac{1}{12}$ ...
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### What are the relative benefits of using Adams-Moulton over Adams-Bashforth algorithm?

I am solving a system of two coupled PDE's in two spatial dimensions and in time computationally. Since the function evaluations are expensive, I would like to use a multistep method (initialised ...
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### Error propagation on GSL eigenvalues computation

The problem comes from the need to estimate the error propagation of the spectral norm computation of a square matrix $A$ of which I know the components' $A_{ij}$ absolute error. The fundamental step ...
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### Estimating hardware error probability

Say I run a supercomputer computation on 100k cores for 4 hours on http://www.nersc.gov/users/computational-systems/edison/configuration, exchanging about 4 PB of data over the network and performing ...
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### Methods for integrating black box functions on a non-uniform grid

If i have some function expressed as points on a non-uniform grid (I'm specifically interested in logarithmic grids, but general results are also interesting), and I want to integrate it, I believe ...
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### a posteriori error estimation for skewed elements

I'm working with error estimates for Poisson's equation of the form $$\mathcal{E}^2_T = h_T^2\|-\Delta u - f\|_{L^2(T)} + \sum_{e\in \partial T} h_e\|n\cdot \nabla u\|_{L^2(e)}$$ where $T$ is an ...
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### Approximating forward Error function

and i have i question. i was given equation $$f(x) = 0$$ $$f(x) = cos(\frac{x}{50}) - \frac{1}{\sqrt{2}}$$ and the approximation root $$x_a$$ such that $$\vert f(x_a)\vert < \epsilon =0.001$$....
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