B-spline Quasi-interpolation Sampling Recovery in Freud-weighted Sobolev Spaces
Introduces equidistant, compact-supported B-spline quasi-interpolation and interpolation sampling operators that recover univariate functions in Freud-weighted Sobolev spaces from finitely many sample values, with error measured in the weighted Lebesgue norm. Students learn how truncated, scaled B-spline (quasi-)interpolation attains the asymptotically optimal sampling n-width rate across all L_p-to-L_q settings and yields the matching optimal equidistant quadratures for weighted numerical integration on the real line.
Weighted approximate sampling recovery and integration based on B-spline interpolation and
This paper constructs equidistant, compact-supported B-spline quasi-interpolation and interpolation sampling algorithms (denoted Q_rho,m and P_rho,m) for the approximate recovery and numerical integr…