Cross-Product Cubature Error Bounds

Cubature Error Bounds for Analytic Functions

In this paper, two-dimensional cubature error bounds are developed. It is assumed that the function to be integrated is analytic, and that the domain of integration is contained in [—1, 1] X [—1, 1]. Tables of error constants for several cubature rules and domains of integration are included.

Numerical Cubature Using Error-Correcting Codes

We present a construction for improving numerical cubature formulas with equal weights and a convolution structure, in particular equal-weight product formulas, using linear error-correcting codes. The construction is most effective in low degree with extended BCH codes. Using it, we obtain several sequences of explicit, positive, interior cubature formulas with good asymptotics for each fixed ...

Error Estimates for Polyharmonic Cubature Formulas

In the present article we shall present basic features of a polyharmonic cubature formula of degree s and corresponding error estimates. Main results are Markov-type error estimates for differentiable functions and error estimates for functions f which possess an analytic extension to a sufficiently large ball in the complex space Cd . 2000 AMS subject classification: 65D30, 32A35

Regularization Path of Cross-Validation Error Lower Bounds

Careful tuning of a regularization parameter is indispensable in many machine learning tasks because it has a significant impact on generalization performances. Nevertheless, current practice of regularization parameter tuning is more of an art than a science, e.g., it is hard to tell how many grid-points would be needed in cross-validation (CV) for obtaining a solution with sufficiently small ...

On the Smolyak cubature error for analytic functions