Główne pojęcia
가중 최소 ℓp 근사법의 이론과 최적성에 대한 연구
Statystyki
A∥Q∥p Lp(M) ≤ Nn ∑k=1 τn,k|Q(xn,k)|p ≤ B∥Q∥p Lp(M)
∥f − LMn(f)∥L2(M) ≤ c(1 + κ2)1/2n−r+d/2∥f∥Hr(M)
Z M f(x)dν(x) − In(f) ≤ c(1 + κ1/2)n−r+d/2∥f∥Hr(M)
Cytaty
"Firstly, the least squares quadrature rules were derived from Marcinkiewicz-Zygmund inequalities in L2 by means of frame theory, whereas traditional quadrature rules were often associated with Marcinkiewicz-Zygmund inequalities in L1."
"Secondly, the obtained error for the Sobolev spaces with smoothness index r is O(n−r+d/2), which is almost optimal, and the constants depend only on the global condition number κ of the L2-Marcinkiewicz-Zygmund family."
"Thirdly, the proofs were based on the hypothesis of Weyl’s law, which is related to the critical Sobolev exponent and leads to explicit and transparent error estimates."