By R. A. Hill

ISBN-10: 0198538030

ISBN-13: 9780198538035

The purpose of this publication is to supply an straight forward therapy of the speculation of error-correcting codes, assuming not more than highschool arithmetic and the power to hold out matrix mathematics. The publication is meant to function a self-contained path for moment or 3rd 12 months arithmetic undergraduates, or as a readable creation to the mathematical facets of coding for college students in engineering or desktop technology.

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**Sample text**

3 Computing the Proximal Operator Computing the proximal operator eﬃciently and exactly is crucial to enjoying the fast convergence rates of proximal methods. We therefore focus here on properties of this operator and on its computation for several sparsityinducing norms. Dual proximal operator. 13): maxp − v∈R 1 2 v−u 2 2 − u 2 such that Ω∗ (v) ≤ μ. 3 (Relation to dual proximal operator). Let ProxμΩ be the proximal operator associated with the regularization μΩ, where Ω is a norm, and let Proj{Ω∗ (·)≤μ} be the projector on the ball of radius μ of the dual norm Ω∗ .

Zanni, T. Seraﬁni, and G. Zanghirati. Parallel software for training large scale support vector machines on multiprocessor systems. Journal of Machine Learning Research, 7:1467–1492, 2006. P. Zhao, G. Rocha, and B. Yu. The composite absolute penalties family for grouped and hierarchical model selection. Annals of Statistics, 37(6A):3468–3497, 2009. M. Zinkevich. Online convex programming and generalized inﬁnitesimal gradient ascent. In Proceedings of the 20th International Conference on Machine Learning, pages 928–936, 2003.

4). 17). Indeed, 4. The dual variable from Fenchel duality is −v in this case. 3 Proximal Methods 31 this equation indicates that the proximal operator can be computed on each group g as the residual of a projection on an 1 -norm ball in R|g| ; the latter is done eﬃciently with the previously mentioned linear-time algorithms. In general, the case where groups overlap is more complicated because the regularization is no longer separable. Nonetheless, in some cases it is still possible to compute the proximal operator eﬃciently.

### A First Course in Coding Theory by R. A. Hill

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