Computation of Induced Orthogonal Polynomial Distributions
Computation of Induced Orthogonal Polynomial Distributions
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DOI：
10.1553/etna_vol50s71
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发表时间：
2017-04
期刊：
影响因子：
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通讯作者：
A. Narayan
中科院分区：
文献类型：
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作者：
A. Narayan
我们提供了一个强大的和一般的算法计算相关的诱导正交多项式措施的分布函数。我们利用正交多项式的几个工具，为广泛的一类措施，这是稳定的多项式次数至少达到1000度的光谱精确的方法。与其他标准工具，如数值求根算法和逆变换采样配对，这提供了一种从诱导正交多项式测量生成随机样本的方法。从这个测量生成样本是某些类型的多元多项式近似的最佳数值方法的一个组成部分。例如，加权离散最小二乘近似的诱导分布的采样最近已被证明可以用最少数量的样本产生收敛保证。我们还提供了公开的代码，实现本文中的算法，从诱导分布采样。
We provide a robust and general algorithm for computing distribution functions associated to induced orthogonal polynomial measures. We leverage several tools for orthogonal polynomials to provide a spectrally-accurate method for a broad class of measures, which is stable for polynomial degrees up to at least degree 1000. Paired with other standard tools such as a numerical root-finding algorithm and inverse transform sampling, this provides a methodology for generating random samples from an induced orthogonal polynomial measure. Generating samples from this measure is one ingredient in optimal numerical methods for certain types of multivariate polynomial approximation. For example, sampling from induced distributions for weighted discrete least-squares approximation has recently been shown to yield convergence guarantees with a minimal number of samples. We also provide publicly-available code that implements the algorithms in this paper for sampling from induced distributions.