# Questions tagged [error-estimation]

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### Round-off errors in ratio of Gaussian functions

I would like to understand how division of round-off errors can lead to large errors??? I am using a method to measure the frequency dependent dissipation in simulations performed by Discontinuous ...
37 views

### Deterministic method to compute “Process noise covariance matrix, Q” for a Kalman filter when parameter variations of the model is known apriori

I am implementing a Kalman filter (for a linear ODE system for now). My model represents a physical device that has 6 "parameters", i.e. those values of the device do not evolve over time (within a ...
115 views

### Precision not improving by decreasing step-size in nonlinear Schrödinger

I tried to simulate soliton propagation by solving the nonlinear Schrödinger equation using the split-step Fourier method. The following is an example of the Matlab code copied from a textbook. ...
47 views

### Quick evaluation of floating point Absolute Error

I need to to find a quick and dirty way to estimate the absolute error introduced by a series of agebraic operations of IEEE single precision floating point numbers, a pessimistic result is ok. The ...
49 views

### 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 ...
84 views

### function over conditional probability

I need to create a scoring model out of estimated conditional probability functions for two events, A and B. Let 0.5 be the threshold value. Ideally, the probability is in the interval $[0,0.5)$ for A ...
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### Numerical analysis: Chebyshev coefficient representation error

If $x_k$ are the Chebyshev nodes, that is for $n \in \mathbb{N}^*$, we have $x_k = \cos(\pi \frac{2k + 1}{n})$. Now suppose you have approximated values of $x_k$ and $x_{k'}$ for $k,k' \leq n$. In the ...
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### Procedure to identify characteristic properties of unknown functions in a DAE model

I have a system of 1st order odes given by $$\dot{x_1}(t) = \alpha_1 f_1(x_1,t) + \beta_1 u(t) \\ \dot{x_2}(t) = \alpha_2 f_2(x_2,t) + \beta_2 u(t)$$ They are constrained by an algebraic equation ...
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### How group similar data in a single classes and reduce the error

I have vehicles gps information in my real time traffic application. Averaging that information I know the speed of every road at any time. The problem is that is too much data to send back to the ...
188 views

### Estimate $L_2$ norm of a elliptic problem with unknown exact solution on finite element method

I have the elliptic problem $$-\Delta u = 1,\,\,\Omega\subset\mathbb{R}^2$$ with $u=0$ on $\partial\Omega,$ with $\Omega=[-1,1]^2\backslash([0,1]\times[-1,0])$ and I want to estimate the $L_2$ error ...
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### Gradient convergence on a checkerboard domain in finite element

I've got an elliptic problem in a domain with two materials in a checkerboard arrangement. Both materials are highly dissimilar, being one much more compliant than the other. If I use classic linear ...
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### Error in Monte Carlo integration

I am looking for a concise description to help me understand the error for Monte Carlo Integration using Uniform Sampling and Importance Sampling For Importance Sampling I have that the error is just ...
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### Error analysis of Modified Lentz's method

In Numerical Recipes, the authors state: There is at present no rigorous analysis of error propagation in Lentz’s algorithm. This statement is now ~15 years old, so I wonder has this gap in the ...
Lets say we have two things as input, $N$ scalars (measurements) that we know are erroneous to some degree (i.e. the correct values are somewhat similar). In addition, we also have a roughly more ...