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Numerical analysis

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Abstract In this article, we touch on a few selected topics illustrating the interplay between computational statistics and numerical analysis. Rather than briefly reviewing a long array of methods, on one hand we place emphasis on problems, such as stochastic optimization, which require the joint application of several techniques; on the other hand, we stress a few recurring themes such as conditioning, numerical stability, convergence, and different discretization approaches that are at the root of many numerical methods. Then, we examine some forms of function approximation, the solution of algebraic and functional equations, and numerical quadrature. In particular, we outline some possibly less familiar topics, such as homotopy continuation and collocation methods. WIREs Comp Stat 2011 3 434–449 DOI: 10.1002/wics.172 This article is categorized under: Algorithms and Computational Methods > Dynamic Programming Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC) Algorithms and Computational Methods > Numerical Methods

A regular grid to discretize a rectangular domain.

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A deterministic, nonregular sample based on low‐discrepancy sequences.

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A pseudorandom sample.

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Tackling a nonconvex objective function: its convexification and a convex lower bound.

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An illustration of Kelley's cutting plane algorithm.

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A cubic spline yields a smoother interpolant than higher order polynomials.

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Oscillations in a high‐order interpolating polynomial.

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Algorithms and Computational Methods > Numerical Methods
Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC)
Algorithms and Computational Methods > Dynamic Programming

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