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SIAM Journal on Numerical Analysis, 2003

Groff, R. E.Pramod, P. P.
Koditschek, D. E.
Electrical and Computer Engineering
ECE Department, University of Florida
Department of Electrical and Systems Engineering, University of Pennsylvania

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Abstract
The class of continuous piecewise linear (PL) functions represents a useful family of approximants because invertibility can be readily imposed, and if a PL function is invertible, then it can be inverted in closed form. Many applications, arising, for example, in control systems and robotics, involve the simultaneous construction of a forward and inverse system model from data. Most approximation techniques require that separate forward and inverse models be trained, whereas an invertible continuous PL affords, simultaneously, the forward and inverse system model in a single representation. The minvar algorithm computes a continuous PL approximation to data. Local convergence of minvar is proven for the case when the data generating function is itself a PL function and available directly rather than through data.
BibTeX entry
@inproceedings{SIAM Journal on Numerical Analysis, 2003,
  author = {GROFF R. E. and KHARGONEKAR, P. P. and Koditschek,
	D. E.},
  title = {A Local Convergence Proof for the Minvar Algorithm for Computing Continuous Piecewise Linear Approximations},
  booktitle = {SIAM Journal on Numerical Analysis, 2003, Vol. 41, No. 3, pp. 9831007},
  year = {2003}
}

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