Approximating polynomials

Many problems of practical significance are NPcomplete but are too important to abandon merely because obtaining an optimal solution is intractable (khó). If a problem is NPcomplete, we are unlikely to find a polynomial time algorithm for solving it exactly, but it may still be possible to find nearoptimal solution in polynomial time.
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We give sufficient conditions so that the union of two graphs with CR isolated singularities in C2 is locally polynomially convex at a singularly point. Using this result and some ideas in previous work, we obtain a new result about local approximation continuous function. 1. Introduction ˆ We recall that for a given compact K in Cn , by K we denote the polynomial convex hull of K i.e., ˆ K = {z ∈ Cn : p(z) ≤ p K for every polynomial p in Cn }. ˆ We say that K is polynomially convex if K = K ....
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In this paper we give results about polynomial approximation on the closed polydisk in Cn . 1. Introduction Let X be a compact subset of Cn . By C(X) we denote the space of all continuous complexvalued functions on X, with norm f X = max{f (z) : z ∈ X}, and let P (X) denote the closure of set of polynomials in C(X). The polynomially convex hull of X will ˆ be denoted by X and diﬁned by ˆ X = {z ∈ Cn : p(z) p X for every polynomial p}.
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count instead of explicitly combines features. By setting with polynomial kernel degree (i.e., d), different number of feature conjunctions can be imKernel methods such as support vector maplicitly computed. In this way, polynomial kernel chines (SVMs) have attracted a great deal SVM is often better than linear kernel which did of popularity in the machine learning and not use feature conjunctions. However, the training natural language processing (NLP) comand testing time costs for polynomial kernel SVM munities. ...
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.Leif Mejlbro Real Functions in One Variable Examples of Taylor’s Formula and Limit Processes Calculus 1c6 Download free ebooks at bookboon.com .Real Functions in One Variable  Examples of Taylor’s Formula and Limit Processes  Calculus 1c6 © 2008 Leif Mejlbro & Ventus Publishing ApS ISBN 9788776813932 Download free ebooks at bookboon.com .
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Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí y học Molecular Biology cung cấp cho các bạn kiến thức về ngành sinh học đề tài: A polynomial time biclustering algorithm for finding approximate expression patterns in gene expression time series...
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Calculus 2a Real Functions in Several Variables  Guidelines for Solutions of Some Types of Problems
The purpose of this volume is to give some guidelines for the student concerning the solution of problems in the theory of Functions in Several Variables. The intension is not to write a textbook, but instead to give some hints of how to solve problems in this fi eld. It therefore cannot replace any given textbook, but it may be used as a supplement to such a book on Functions in Several Variables.
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INTRODUCTION In Section 6.3 we developed a recursive leastsquares growing memoryﬁlter for the case where the target trajectory is approximated by a polynomial. In this chapter we develop a recursive leastsquares growingmemory ﬁlter that is not restricted to having the target trajectory approximated by a polynomial [5. pp. 461–482]. The only requirement is that Y nÀi , the measurement vector at time n À i, be linearly related to X nÀi in the errorfree situation. The Y nÀi can be made up to multiple measurements obtained at the time n À i as in (4.
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Timing Adjustment by Interpolation In this chapter we focus on digital interpolation and interpolator control. In Section 9.1 we discuss approximations to the ideal interpolator. We first consider FIR filters which approximate the ideal interpolator in the mean square sense. A particularly appealing solution for high rate applications will be obtained if the dependency of each filter tap coefficient on the fractional delay is approximated by a polynomial in the fractional delay. It is shown that with loworder polynomials excellent approximations are possible. In Section 9.
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Rational Function Interpolation and Extrapolation Some functions are not well approximated by polynomials, but are well approximated by rational functions, that is quotients of polynomials. We denote by Ri(i+1)...(i+m) a rational function passing through the m + 1 points (xi , yi ) . . . (xi+m , yi+m ). More explicitly, suppose Ri(i+1)...(i+m) = p 0 + p1 x + · · · + pµ x µ Pµ (x) = Qν (x) q 0 + q 1 x + · · · + q ν xν (3.2.1)
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In §5.8 and §5.10 we learned how to ﬁnd good polynomial approximations to a given function f (x) in a given interval a ≤ x ≤ b. Here, we want to generalize the task to ﬁnd good approximations that are rational functions (see §5.3).
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We discuss the use of social networks in implementing viral marketing strategies. While influence maximization has been studied in this context (see Chapter 24 of [10]), we study revenue maximization, arguably, a more natural objective. In our model, a buyer’s decision to buy an item is influenced by the set of other buyers that own the item and the price at which the item is offered. We focus on algorithmic question of finding revenue maximizing marketing strategies. When the buyers are completely symmetric, we can find the optimal marketing strategy in polynomial time.
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Annals of Mathematics In this paper we will solve one of the central problems in dynamical systems: Theorem 1 (Density of hyperbolicity for real polynomials). Any real polynomial can be approximated by hyperbolic real polynomials of the same degree. Here we say that a real polynomial is hyperbolic or Axiom A, if the real line is the union of a repelling hyperbolic set, the basin of hyperbolic attracting periodic points and the basin of inﬁnity.
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Let G be a graph with vertex set V (G) = {1, . . . , n} and edge set E(G). We are interested in studying the functions of the graph G whose values belong to the interval [(G), (G)]. Here (G) is the size of the largest stable set in G and (G) is the smallest number of cliques that cover the vertices of G. It is well known (see, for example, [1]) that for some 0 it is impossible to approximate in polynomial time (G) and (G) within a factor of n, assuming P 6= NP. We suppose that better approximation could...
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In this paper the spline approximation was applied to the empirical vertical profiles of oceanographic parameters such as temperature, salinity or density to obtain a more precise and reliable result of interpolation. Our experiments with the case of observed temperature profiles in Eastern Sea show that the cubic polynomial spline method has a higher reliability and precision in a comparison with the linear interpolation and other traditional methods. The method was realized as a subroutine in our programs for oceanographic data management and manipulation.
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That is all: just a computer procedure to approximate a real root. From the narrow perspective of treating mathematics as a tool to solve real life problems, this is of course suﬃcient. However, from the point of view of mathematics, shouldn’t a student be interested in roots of polynomials in general? Fourth degree? Odd degree? Other roots, once one is found? Rational roots? Total number of roots? Not every detail need be explained, but even the average student will have his life improved by the mere knowledge that there are such questions, often with answers, e.g.
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