INTERMEDIATE ERROR-ESTIMATES

[摘要] Let R[f] be the remainder of some approximation method, having estimates of the form \R[f]\ less-than-or-equal-to rho(i) \\ f(i) \\ for i = 0,..., r. In many cases, rho0 and rho(r) are known, but not the intermediate error constants rho1,..., rho(r-1). For periodic functions, Ligun (1973) has obtained an estimate for these intermediate error constants by rho0 and rho(r). In this paper, we show that this holds in the nonperiodic case, too. For instance, the estimates obtained can be applied to the error of polynomial or spline approximation and interpolation, or to numerical integration and differentiation.

[发布日期] 1994-05-20

[效力级别]  Proceedings Paper

[关键词] ERROR ESTIMATES;INTERMEDIATE ERROR CONSTANTS;JACKSON-TYPE ESTIMATES;ROMBERG QUADRATURE