Abstract
The first chapter provides an account of basic facts on approximation by algebraic and trigonometric polynomials introducing the most important concepts on approximation of functions. In Sect. 1.1 we introduce the basic notions, a connection between algebraic and trigonometric polynomials, best approximation by polynomials and give an account on Chebyshev polynomials, Chebyshev extremal problems, Chebyshev alternation theorem, as well as some numerical methods and examples. Basic facts on trigonometric approximation are given in Sect. 1.2, including moduli of smoothness, best approximation and Besov spaces. Chebyshev systems and interpolation processes are considered in Sect. 1.3. Especially, in Sect. 1.4 we give basic results on interpolation by algebraic polynomials, including representations and computation of interpolation polynomials, Lagrange operators, interpolation errors and uniform convergence in some important classes of functions, as well as an account on the Lebesgue function and some estimates for the Lebesgue constant. Finally, an algorithm for finding optimal nodes is presented.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
