Polynomial approximation problems

Part 1 book "Numerical methods for engineers" includes content: Mathematical modeling and engineering problem solving; programming and software; approximations and round off errors; truncation errors and the Taylor series; bracketing methods; open methods- roots of polynomials; case studies - roots of equations; Gauss elimination; Lu decomposition and matrix inversion; special matrices and Gauss seidel; case studies - linear algebraic; one dimensional unconstrained optimization; multidimensional unconstrained optimization; constrained optimization; case studies - optimization.

456p muasambanhan06 01-02-2024 5 1   Download

Theory of Computation: Lecture 34. The main topics covered in this lesson include: three versions of the TSP problem; an approximation algorithm for the TSP problem; space complexity; polynomial time algorithm; the euclidean TSP;...

33p andromedashun 26-05-2022 9 1   Download

This paper investigates the possibility of using an efficient high-order polynomial element in the SBFEM to form the approximation in the circumferential direction. The governing equations are formulated from the classical linear elasticity theory via the SBFEM technique.

14p inception36 30-11-2021 6 1   Download

The longest path problem is known to be NP-hard. Moreover, it cannot be approximated within a constant ratio, unless P = NP. The best known polynomial time approximation algorithms for this problem essentially find a path of length that is the logarithm of the optimum.

12p vinaruto2711 05-04-2019 39 0   Download

In the present work we prove some direct and inverse theorems for approximation by trigonometric polynomials in Musielak–Orlicz spaces. Furthermore, we get a constructive characterization of the Lipschitz classes in these spaces.

20p nutifooddau 21-01-2019 14 2   Download

In this paper, a new approach for solving space fractional order diffusion equations is proposed. The fractional derivative in this problem is in the Caputo sense. This approach is based on shifted Chebyshev polynomials of the fourth kind with the collocation method.

15p danhdanh27 07-01-2019 32 1   Download

The paper presents a comparison between three approaches to solving the length-bounded maximum multicommodity flow problem with unit edge-lengths. Following the first approach, Garg and Konemann’s, we developed an improved fully polynomial time approximation scheme for this problem. As the second alternative, we considered the well-known greedy approach.

20p danhnguyentuongvi27 19-12-2018 14 0   Download

The fact that polynomial time algorithm is very unlikely to be devised for an optimal solving of the NP-hard problems strongly motivates both the researchers and the practitioners to try to solve such problems heuristically, by making a trade-off between computational time and solution’s quality.

38p vinguyentuongdanh 19-12-2018 38 1   Download

The purpose of this paper is to study the approximability of two non-linear Knapsack problems, which are motivated by important applications in alternating current electrical systems. The first problem is to maximize a nonnegative linear objective function subject to a quadratic constraint, whilst the second problem is a dual version of the first one, where an objective function is minimized.

15p thuyliebe 05-10-2018 29 0   Download

(bq) part 1 book "numerical analysis" has content: mathematical preliminaries and error analysis, solutions of equations in one variable, interpolation and polynomial approximation, numerical differentiation and integration, initial value problems for ordinary differential equations, direct methods for solving linear systems.

446p bautroibinhyen19 02-03-2017 53 5   Download

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.

334p dacotaikhoan 25-04-2013 32 3   Download

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.

10p doiroimavanchuadc 06-02-2013 57 6   Download

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.

39p noel_noel 17-01-2013 48 5   Download

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.

91p sn_buon 29-11-2012 71 4   Download

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 NP-complete, we are unlikely to find a polynomial time algorithm for solving it exactly, but it may still be possible to find near-optimal solution in polynomial time.

22p lucky156 04-06-2010 209 18   Download