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The Output Least Squares Identifiability of the Diffusion Coefficient from an H1–Observation in a 2–D Elliptic Equation

Guy Chavent, Karl Kunisch (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Output least squares stability for the diffusion coefficient in an elliptic equation in dimension two is analyzed. This guarantees Lipschitz stability of the solution of the least squares formulation with respect to perturbations in the data independently of their attainability. The analysis shows the influence of the flow direction on the parameter to be estimated. A scale analysis for multi-scale resolution of the unknown parameter is provided.

The role of parameter constraints in EE and OE methods for optimal identification of continuous LTI models

Witold Byrski, Jedrzej Byrski (2012)

International Journal of Applied Mathematics and Computer Science

The paper presents two methods used for the identification of Continuous-time Linear Time Invariant (CLTI) systems. In both methods the idea of using modulating functions and a convolution filter is exploited. It enables the proper transformation of a differential equation to an algebraic equation with the same parameters. Possible different normalizations of the model are strictly connected with different parameter constraints which have to be assumed for the nontrivial solution of the optimal...

The UD RLS algorithm for training feedforward neural networks

Jarosław Bilski (2005)

International Journal of Applied Mathematics and Computer Science

A new algorithm for training feedforward multilayer neural networks is proposed. It is based on recursive least squares procedures and U-D factorization, which is a well-known technique in filter theory. It will be shown that due to the U-D factorization method, our algorithm requires fewer computations than the classical RLS applied to feedforward multilayer neural network training.

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