منابع مشابه
Minimax Polynomial Approximation
Some new methods for obtaining the minimax polynomial approximation of degree n to a continuous function are introduced, and applied to several simple functions. The amount of computation required is substantially reduced compared with that of previous methods.
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The need to solve a polynomial minimax approximation problem appears often in science. It is especially common in signal processing and in particular in filter design. The results presented in this paper originated from a study of the finite wordlength restriction in the FIR digital filter design problem. They are, however, much more general and can be applied to any polynomial minimax approxim...
متن کاملPolynomial Approximation
Polynomials are very simple mathematical functions which have the flexibility to represent very general nonlinear relationships. Approximation of more complicated functions by polynomials is a basic building block for many numerical techniques. This article considers two distinct but related applications. The first is polynomial regression in which polynomials are used to model a nonlinear rela...
متن کاملLocal Minimax Learning of Approximately Polynomial Functions
Suppose we have a number of noisy measurements of an unknown real-valued function f near a point of interest x0 ∈ R. Suppose also that nothing can be assumed about the noise distribution, except for zero mean and bounded covariance matrix. We want to estimate f at x0 using a general linear parametric family f(x; a) = a0h0(x) + . . . + aqhq(x), where a ∈ R and hi’s are bounded functions on a nei...
متن کاملStrategyproof Approximation of the Minimax on Networks
We consider the problem of locating a facility on a network represented by a graph. A set of strategic agents have different ideal locations for the facility; the cost of an agent is the distance between its ideal location and the facility. A mechanism maps the locations reported by the agents to the location of the facility. We wish to design mechanisms that are strategyproof (SP) in the sense...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1966
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1966-0195235-8