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Algorithms and error bounds for multivariate piecewise constant approximation

Davydov, Oleg (2011) Algorithms and error bounds for multivariate piecewise constant approximation. In: Approximation Algorithms for Complex Systems. Springer-Verlag, Heidelberg, pp. 27-45. ISBN 9783642168758

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We review the surprisingly rich theory of approximation of functions of many vari- ables by piecewise constants. This covers for example the Sobolev-Poincar´e inequalities, parts of the theory of nonlinear approximation, Haar wavelets and tree approximation, as well as recent results about approximation orders achievable on anisotropic partitions.