On the Kaczmarz algorithm of approximation in infinite-dimensional spaces

• Autorzy: Stanisław Kwapień , Jan Mycielski
• Języki publikacji: EN

Abstrakty

EN

The Kaczmarz algorithm of successive projections suggests the following concept. A sequence $(e_{k})$ of unit vectors in a Hilbert space is said to be effective if for each vector x in the space the sequence (xₙ) converges to x where (xₙ) is defined inductively: x₀ = 0 and $xₙ = x_{n-1} + αₙeₙ$, where $αₙ = ⟨x - x_{n-1},eₙ⟩$. We prove the effectivity of some sequences in Hilbert spaces. We generalize the concept of effectivity to sequences of vectors in Banach spaces and we prove some results for this more general concept.

Kategorie tematyczne

• 60G25: Prediction theory
• 41A65: Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
• 60H25: Random operators and equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 148
• Numer: 1
• Strony: 75-86

Daty

wydano

2001

Twórcy

autor

Stanisław Kwapień

• Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

autor

Jan Mycielski

• Department of Mathematics, University of Colorado, Boulder, CO 80309-0395, U.S.A.

Identyfikatory

DOI

10.4064/sm148-1-7