#### Filter Results:

- Full text PDF available (48)

#### Publication Year

1993

2017

- This year (2)
- Last 5 years (12)
- Last 10 years (25)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

- H. N. Mhaskar
- 1996

We prove that neural networks with a single hidden layer are capable of providing an optimal order of approximation for functions assumed to possess a given number of derivatives, if the activation function evaluated by each principal element satisfies certain technical conditions. Under these conditions, it is also possible to construct networks that… (More)

- Hrushikesh Narhar Mhaskar, Francis J. Narcowich, Joseph D. Ward
- Math. Comput.
- 2001

Geodetic and meteorological data, collected via satellites for example , are genuinely scattered, and not confined to any special set of points. Even so, known quadrature formulas used in numerically computing integrals involving such data have had restrictions either on the sites (points) used or, more significantly, on the number of sites required. Here,… (More)

- Hrushikesh Narhar Mhaskar
- Adv. Comput. Math.
- 1993

- M. Maggioni, H. N. Mhaskar
- 2006

We construct a multiscale tight frame based on an arbitrary orthonormal basis for the L 2 space of an arbitrary sigma finite measure space. The approximation properties of the resulting multiscale are studied in the context of Besov approximation spaces, which are characterized both in terms of suitable K–functionals and the frame transforms. The only major… (More)

- Hrushikesh Narhar Mhaskar, Francis J. Narcowich, Joseph D. Ward
- Adv. Comput. Math.
- 1999

A zonal function (ZF) network is a function of the form x → n k=1 c k φ(x · y k), where x and the y k 's are on the on the unit sphere in q + 1 dimensional Euclidean space, and where the y k 's are scattered points. In this paper, we study the degree of approximation by ZF networks. In particular, we compare this degree of approximation with that obtained… (More)

- Hrushikesh Narhar Mhaskar
- J. Complexity
- 2004

Let q ≥ 1 be an integer, Q be a Borel subset of the Euclidean space R q , µ be a probability measure on Q, and F be a class of real valued, µ-integrable functions on Q. The complexity problem of approximating fdµ using quasi-Monte Carlo methods is to estimate sup f ∈F fdµ − 1 n n k=1 f (x k) The problem is said to be tractable if there exist constants c, α,… (More)

- Hrushikesh Narhar Mhaskar
- Journal of Approximation Theory
- 2004

We obtain a characterization of local Besov spaces of functions on [−1, 1] in terms of algebraic polynomial operators. These operators are constructed using the coefficients in the orthogonal polynomial expansions of the functions involved. The example of Jacobi polynomials is studied in further detail. A by-product of our proofs is an apparently simple… (More)

- Charles K. Chui, Xin Li, Hrushikesh Narhar Mhaskar
- Adv. Comput. Math.
- 1996

- H. N. Mhaskar, J. Prestin
- 2000

We propose a class of algebraic polynomial frames, which are computationally easier to implement than polynomial bases. We also discuss the weighted L p-stability of our frames for 1 ≤ p ≤ ∞. Our analysis is based on orthogonal polynomials with respect to the weight in question, but the frame bounds are independent of the system of orthogonal polynomials… (More)

For the unit sphere embedded in a Euclidean space, we obtain quadrature formulas that are exact for spherical harmonics of a fixed order, have nonnegative weights, and are based on function values at scattered points (sites). The number of scattered sites required is comparable to the dimension of the space for which the quadrature formula is required to be… (More)