# Questions tagged [error-estimation]

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### Normalizing error when data passes through zero

Given a time-dependent measure of error, $e(t)$, and a time-dependent function to normalize it with, $f(t)$, one would report the normalized error as $$E(t) = \left|\frac{e(t)}{f(t)}\right|.$$ ...
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### How can you calculate percent error in tensor approximations?

I have a matrix A which is an approximation to the known matrix B. Both matrices are square, 3x3 matrices and, in this case, are ...
134 views

### Convergence of adaptive finite elements with inexact solves

I'm working on some adaptive discontinuous Galerkin codes for time harmonic wave propagation, currently just Helmholtz, but will be branching out once I have a working prototype in this case. There ...
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### Known Algorithm to compute errors of given nature

I have three sets of data, measured by three different devices: A,B and C of air balloon whose fall is influenced by wind and ...
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### Error bars for pair-correlation function

I have obtained some data from neutron diffraction for some material samples. The "rawest" form of the data is the structure function $S(Q)$. We can choose a variety of different Q-maxes when ...
199 views

### How can I quantify the error of FFT-based poisson solvers?

I have an FFT code that solves a particular case of the steady Euler equations where a Poisson equation is solved, what is a good way to quantify the error? Is what I am doing ok? Since I do not have ...
208 views

### Problem Condition and Algorithm Stability

Consider 2 mathematical problems: $$f_1(x) = a - x \\ f_2(x) = e^x -1$$ The condition number for a function is defined as follows: $$k(f) = \left| x \cdot \frac{f'}{f} \right|$$ Lets analyze ...
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### Why do equi-spaced points behave badly?

Experiment description: In Lagrange interpolation, the exact equation is sampled at $N$ points (polynomial order $N - 1$) and it is interpolated at 101 points. Here $N$ is varied from 2 to 64. Each ...
230 views

### Error analysis of WENO scheme

I have three questions regarding WENO schemes 1) How to actually compute the smoothness indicators $\beta_j$ for required order of polynomial? Any reference which explains the algorithm will be ...
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Most numerical methods for quadrature treat the integrand as a black-box function. What if we have more information? In particular, what benefit, if any, can we derive from knowing the first few ...
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### Propogated Error in Mesh Interpolation

I am working with a code that solves diffusion/reaction equations on a 2D unstructured mesh. Due to the stiffness of some of the processes, I start with time steps near 1e-13, and end with a final ...