Tractability of Multivariate Problems

By Erich Novak, Henryk Wozniakowski. 2008

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In Numerical Analysis

Citations in the corpus

Convergence guarantees for kernel-based quadrature rules in misspecified settings (2016, background): “W Kor([0, 1]) consists of periodic functions on [0, 1] whose derivatives up to (α − 1)-th are absolutely continuous and the α-th derivative belongs to L2([0, 1]) [16].”
Hyperbolic Cross Approximation (2016, background): “The following list contains monographs and survey papers directly related to this book: [206], [345], [322], [357], [71], [370], [47], [70], [255], [256], [257], [82], [251], [283].”
Spline interpolation on sparse grids (2011, background): “See for instance the recent monographs of Novak and Woźniakowski [1,2].”
Approximation of eigenfunctions in kernel-based spaces (2014, unknown): “The result can be found in [17].”
Mercer’s Theorem on General Domains: On the Interaction between Measures, Kernels, and RKHSs (2012, unknown): “the books [21, 28, 29, 30, 2, 26, 1, 3, 44, 22] and the references therein.”
Convergence Types and Rates in Generic Karhunen-Loève Expansions with Applications to Sample Path Properties (2014, background): “g kernel Hilbert spaces (RKHSs), and their interaction with measures from [34]. To this end, let (T,B,ν) be a measure space and k : T × T → Rbe a measurable (reproducing) kernel with RKHS H, see e.g. [23, 30, 31, 27, 37, 33, 24] for more information about these spaces. Recall that in this case the R”
Discrepancy Theory and Quasi-Monte Carlo Integration (2014, unknown): “For a more detailed discussion of tractability of various notions of discrepancy we refer to the work of Novak and Woźniakowski [82, 83, 84, 85].”
Low-rank tensor methods for linear systems and eigenvalue problems (2012, background): “This is to be expected, as isotropic smoothness is not sufficient for tractability of a multivariate problem [59], i.”