Best approximation and numerical methods in solution of differential equations

✍ Scribed by E.G. Litinsky

• Publisher: Elsevier Science
• Year: 1978
• Tongue: English
• Weight: 210 KB
• Volume: 4
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/0771-050x(78)90035-9

✦ Synopsis

Let Q(x) be polynomial of degree q interpolating x m at the points x-i, i = 0, 1, ..., q, where xi are zeros of the Tchebysheff polynomial of degree q + 1 on the interval [0, 1]. If q is of order x/m, then Q(x) approximates x m well enough. This result is used to obtain a good approximation to the solution of a system of linear differential equations.