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Applicable Analysis
An International Journal
Volume 93, 2014 - Issue 10
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Articles

Parallel methods for regularizing systems of equations involving accretive operators

Pham Ky AnhDepartment of Mathematics, Vietnam National University, Hanoi, 334 Nguyen Trai, Thanh Xuan, Hanoi10000, Vietnam.Correspondence[email protected]
,
Nguyen BuongVietnamese Academy of Science & Technology, Institute of Information Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi10000, Vietnam.
&
Dang Van HieuDepartment of Mathematics, Vietnam National University, Hanoi, 334 Nguyen Trai, Thanh Xuan, Hanoi10000, Vietnam.
Pages 2136-2157 | Received 21 Sep 2013, Accepted 22 Nov 2013, Published online: 20 Jan 2014

References

  • Haltmeier M, Kowar R, Leitao A, Scherzer O. Kaczmarz methods for regularizing nonlinear ill-posed equations, I. Convergence analysis. Inverse Prob. Imaging. 2007;1:289–298.
  • Haltmeier M, Kowar R, Leitao A, Scherzer O. Kaczmarz methods for regularizing nonlinear ill-posed equation, II. Applications. Inverse Prob. Imaging. 2007;1:507–523.
  • Burger M, Kaltenbacher B. Regularizing Newton–Kaczmart methods for nonlinear ill-posed problems. SIAM J. Numer. Anal. 2006;44:153–182.
  • De Cezaro A, Haltmeier M, Leitao A, Scherzer O. On steepest-descent-Kaczmarz method for regularizing systems of nonlinear ill-posed equations. Appl. Math. Comput. 2008;202:596–607.
  • Anh PK, Chung CV. Parallel iterative regularization methods for solving systems of ill-posed equations. Appl. Math. Comput. 2009;212:542–550.
  • Anh PK, Chung CV. Parallel regularized Newton method for nonlinear ill-posed equations. Numer. Algor. 2011;58:379–398.
  • Anh PK, Dzung VT. Parallel iteratively regularized Gauss–Newton method. Inter. J. Comput. Math. 2013;90:2452–2461.
  • Anh PK, Chung CV. Parallel hybrid methods for a finite family of relatively nonexpansive mappings. Numer. Funct. Anal. Optim. 2013;doi:10.1080/01630563.2013.830127.
  • Alber YI, Ryazantseva I. Nonlinear ill-posed problems of monotone type. Dordrecht: Spinger; 2006.
  • Diestel J. Geometry of Banach spaces–Selected topics. Lecture notes in mathematics. Vol. 485. Berlin: Springer-Verlag; 1975.
  • Cioranescu I. Geometry of Banach spaces, duality mappings and nonlinear problems. Dordrecht: Kluwer; 1990.
  • Reich S. Review of geometry of Banach spaces, duality mappings and nonlinear problems by Ioana Cioranescu, Kluwer Academic Publishers, Dordrecht, 1990. Bull. Am. Math. Soc. 1992;26:367–370.
  • Reich S. Appoximating zeros of accretive operators. Proc. Am. Math. Soc. 1975;51:381–384.
  • Ball K, Carlen E, Lieb E. Sharp uniform convexity and smoothness inequalities for trace norms. Invent. Math. 1994;115:463–482.
  • Alber YI. New results in fixed point theory. Technion. Unpublished work.
  • Alber YI. On the stability of iterative approximations to fixed point of nonexpansive mappings. J. Math. Anal. Appl. 2007;328:958–971.
  • Xu HK. Viscosity approximation methods for nonexpensive mappings. J. Math. Anal. Appl. 2004;289:279–291.
  • Wang J, Li J, Liu Z. Regularization methods for nonlinear ill-posed problems with accretive operators. Acta Math. Sci. 2008;28:141–150.
  • Blaschke B, Neubauer A, Schezer O. On convergence rates for the iteratively regularized Gauss–Newton method. IMA J. Numer. Anal. 1997;17:421–436.
  • Buong N, Phuong NTH. Convergence rates in regularization for nonlinear ill-posed equations involving m-accretive mappings in Banach spaces. Appl. Math. Sci. 2012;63:3109–3117.
  • Alber YI, Chidume CE, Zegeye H. Regularization of nonlinear ill-posed equations with accretive operators. Fixed Point Theor. Appl. 2005;2005:11–33.

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