zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A note on the $CQ$ algorithm for the split feasibility problem. (English) Zbl 1080.65033
The authors present modifications to the $CQ$ algorithm proposed by {\it Ch. Byrne} [Inverse Probl. 18, No. 2, 441--453 (2002; Zbl 0996.65048)] and to the relaxed $CQ$ algorithm proposed by {\it Q. Z. Yang} [Inverse Probl. 20, 1261--1266 (2004; Zbl 1066.65047)] to solve the split feasibility problem $x^{k+1}=P_C(x^k-yA^T(P_Q-I)Ax^k)$ by adopting Armijo-like searches. The modified algorithm need not compute matrix inverses and the largest eigenvalue of the matrix $A^TA$. It provides a sufficient decrease of the objective function at each iteration by a judicious choice of the stepsize and can identify the existence of solutions by the iterative sequence. The convergence of the modified algorithms is established under mild conditions.

65F30Other matrix algorithms
65F10Iterative methods for linear systems
Full Text: DOI