DOI: 10.1007/bf02551235. Error bounds for the method of alternating projections

Error bounds for the method of alternating projections

10.1007/bf02551235

Crossref journal-article

Springer Science and Business Media LLC

Mathematics of Control, Signals, and Systems (297)

Bibliography

Kayalar, S., & Weinert, H. L. (1988). Error bounds for the method of alternating projections. Mathematics of Control, Signals, and Systems, 1(1), 43â59.

Authors 2

Selahattin Kayalar (first)
Howard L. Weinert (additional)

References 22 Referenced 69

[AA] V. M. Adamyan and D. Z. Arov, A general solution of a problem in linear prediction of stationary processes,Theory Probab. Appl.,13 (1968), 394–407. (10.1137/1113049) / Theory Probab. Appl. by V. M. Adamyan (1968)
[A] N. Aronszain, Theory of reproducing kernels,Trans. Amer. Math. Soc.,68 (1950), 337–404. (10.1090/S0002-9947-1950-0051437-7) / Trans. Amer. Math. Soc. by N. Aronszain (1950)
[C] Y. Censor, Finite series-expansion reconstruction methods,Proc. IEEE,71 (1983), 409–419. (10.1109/PROC.1983.12598) / Proc. IEEE by Y. Censor (1983)
F. Deutsch, Applications of von Neumann's alternating projections algorithm, inMathematical Methods in Operations Research (P. Kendrov, ed.), pp. 44–51, Sofia, 1983.
[D2] F. Deutsch, Rate of convergence of the method of alternating projections, inParametric Optimization and Approximation (B. Brosowski and F. Deutsch, eds.), pp. 96–107, Birkhauser, Basel, 1985. / Parametric Optimization and Approximation by F. Deutsch (1985)
C. Franchetti and W. Light, On the von Neumann Alternating Algorithm in Hilbert Space, Report 28, Center for Approximation Theory, Texas A&M University, 1982.
[F] K. Friedrichs, On certain inequalities and characteristic value problems for analytic functions and for functions of two variables,Trans. Amer. Math. Soc.,41 (1937), 321–364. (10.1090/S0002-9947-1937-1501907-0) / Trans. Amer. Math. Soc. by K. Friedrichs (1937)
[H] I. Halperin, The product of projection operators,Acta Sci. Math.,23 (1962), 96–99. / Acta Sci. Math. by I. Halperin (1962)
[HS] C. Hamaker and D. C. Solmon, The angles between the null spaces of X-rays,J. Math. Anal. Appl.,62 (1978), 1–23. (10.1016/0022-247X(78)90214-7) / J. Math. Anal. Appl. by C. Hamaker (1978)
[I] S. Ivansson, Seismic borehole tomography—theory and computational methods,Proc. IEEE,74 (1986), 328–338. (10.1109/PROC.1986.13459) / Proc. IEEE by S. Ivansson (1986)
[J] C. Jordan, Essay on the geometry ofn dimensions,Bull. Soc. Math. France,3 (1875), 103–174. (10.24033/bsmf.90) / Bull. Soc. Math. France by C. Jordan (1875)
S. Kaczmarz, Angenaherte auflosung von systemen linearer gleichungen,Bull. Acad. Polon. Sci. Lett.,A (1937), 355–357.
[K2] T. Kato,A Short Introduction to Perturbation Theory for Linear Operators, Springer-Verlag, New York, 1982. (10.1007/978-1-4612-5700-4) / A Short Introduction to Perturbation Theory for Linear Operators by T. Kato (1982)
[N1] H. Nakano,Spectral Theory in Hilbert Space, Japanese Society for the Promotion of Science, Tokyo, 1953. / Spectral Theory in Hilbert Space by H. Nakano (1953)
[N2] J. von Neumann, On rings of operators. Reduction theory,Ann. of Math.,50 (1949), 401–485. (10.2307/1969463) / Ann. of Math. by J. Neumann von (1949)
[N3] J. von Neumann,Functional Operators, Vol. II, Princeton University Press, Princeton, NJ, 1950. / Functional Operators by J. Neumann von (1950)
[P] M. Pavon, New results on the interpolation problem for continuous-time stationary-increments processes,SIAM J. Control Optim.,22 (1984), 133–142. (10.1137/0322010) / SIAM J. Control Optim. by M. Pavon (1984)
[S1] H. Salehi, On the alternating projections theorem and bivariate stationary stochastic processes,Trans. Amer. Math. Soc.,128 (1967), 121–134. (10.1090/S0002-9947-1967-0214135-5) / Trans. Amer. Math. Soc. by H. Salehi (1967)
[S2] R. R. Stoll,Set Theory and Logic, Dover, New York, 1961. / Set Theory and Logic by R. R. Stoll (1961)
[T] K. Tanabe, Projection method for solving a singular system of linear equations and its applications,Numer. Math.,17 (1971), 203–214. (10.1007/BF01436376) / Numer. Math. by K. Tanabe (1971)
[W] N. Wiener, On the factorization of matrices,Comment. Math. Helv.,29 (1955), 97–111. (10.1007/BF02564273) / Comment. Math. Helv. by N. Wiener (1955)
[Y] D. C. Youla, Generalized image restoration by the method of alternating projections,IEEE Trans. Circuits and Systems,25 (1978), 694–702. (10.1109/TCS.1978.1084541) / IEEE Trans. Circuits and Systems by D. C. Youla (1978)

Dates

Type	When
Created	18 years, 7 months ago (Jan. 5, 2007, 6:34 a.m.)
Deposited	6 years, 3 months ago (May 19, 2019, 5:50 p.m.)
Indexed	4 months, 4 weeks ago (March 31, 2025, 5:44 p.m.)
Issued	37 years, 6 months ago (Feb. 1, 1988)
Published	37 years, 6 months ago (Feb. 1, 1988)
Published Print	37 years, 6 months ago (Feb. 1, 1988)

Funders 0

None

BibTeX

@article{Kayalar_1988, title={Error bounds for the method of alternating projections}, volume={1}, ISSN={1435-568X}, url={http://dx.doi.org/10.1007/bf02551235}, DOI={10.1007/bf02551235}, number={1}, journal={Mathematics of Control, Signals, and Systems}, publisher={Springer Science and Business Media LLC}, author={Kayalar, Selahattin and Weinert, Howard L.}, year={1988}, month=feb, pages={43–59} }

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