A Bibliography of Publications of Andrew Knyazev

Andrew Knyazev Associate Professor

Department of Mathematics

University of Colorado at Denver, P.O. Box 173364, Campus Box 170

Denver, CO 80217-3364 USA

Tel: +1 303 556-8102 FAX: +1 303 556-8550

E-mail: aknyazev@tiger.denver.colorado.edu (Internet)

11 May 2013 Version 1.05

Abstract

This bibliography records publications of Andrew Knyazev.

Title word cross-reference

Algebra [BdG92]. algebraic [Kny92a]. algorithm [BK90, Kny92b]. Algorithms [LBA^{+}84, Kny85, Kny86a, KLS90]. almost [BK92]. analysis [KL83]. Applications [Mar94]. April [BdG92]. architecture [Kny92b]. ascent [KS91]. assumptions [Kny86b]. averaged [BK91a].

Belgium [BdG92]. boundaries [Kny83]. Brussels [BdG92].

characteristics [BK91a]. coefficient [KS89]. coefficients [BKK91, Kny92a]. compactness [Kny86b]. components [BK91b, BK94]. composites [BK91a, BK91b, BK94]. Computation [Kny85, Kny86a, BK91a, BK91b, BK94, KL83]. Conference [KX95]. conjugate [Kny91]. consist [BK91b]. Convergence [Kny87a, KL83, KS88, KS91].

Decomposition [GKM^{+}91, KX95]. decompositions [BKE94]. derivation [Kny87b]. descent [KS88]. different [BK91a, BK91b, BK94]. Differential [GKM^{+}91]. Domain [GKM^{+}91, KX95, BK94].

effective [BK91b]. Efficient [BK91a, BK92]. eigenvalue [Kny87a, Kny87b, KS89, KS91, Kny91, KS93b, KS93a, KS94]. eigenvalues [DK82, DK92, Kny85, Kny86a]. eigenvectors [KL83, Kny85, Kny86a]. elliptic [BK90]. Engineering [KX95]. Equations [GKM^{+}91, BK90, BKK91, BK92]. error [Kny85, Kny86a, Kny86b]. essentially [BK91a, BK91b, BK94]. Estimates [KL83, Kny85, Kny86a, Kny86b, Kny87a, Kny87b, KS91, Kny94]. euclidean [KS88]. exact [KS91].

Fictitious [BK94, BK90]. finding [DK82, DK92, Kny83]. fixed [Kny86b]. flow [BK90]. Fourth [GKM^{+}91].

generalized [KS93b, KS94]. gradient [Kny91, KS93b, KS94]. gradient-type [KS93b, KS94]. Group [DK82].

highly [BKK91]. homogenized [BK91b, BK94].

IMACS [BdG92]. implementation [Kny91, Kny92b]. incompressible [BK92]. indefinite [KS89]. inequality [BKE94]. International [BdG92, GKM^{+}91, KX95]. iteration [KS93a]. iterations [Kny92b]. Iterative [BKK91, BK95, BdG92, Kny92a, BK90, BK92, DK82, DK92, KL83, Kny87a, KS89, KLS90, KS93b, KS94].

Korn [BKE94].

Lamé [BK92]. Lehmann [KLS90]. Linear [BdG92, Kny83, KS89]. lower [DK82, DK92]. lower-order [DK82].

materials [BK91a]. Mathemetical [LBA^{+}84]. matrices [BKE94, KS89]. matrix [Kny83]. media [BK92]. mesh [Kny86a, Kny87a]. method [BK90, BK92, DK82, DK92, Kny86b, KS88, KS91, Kny91]. Methods [BK91b, BK95, BdG92, GKM^{+}91, KX95, Kny87b, Mar94, BKK91, BK94, KL83, Kny83, Kny87a, KS89, KLS90, KS93b, KS93a, KS94]. multiprocessor [Kny92b]. norm [KS88]. Numerical [Mar94].

October [KX95]. optimality [KL83]. order [DK82]. orthogonal [BKE94].

Parallel [LBA^{+}84, Kny92b]. Partial [GKM^{+}91, KS93b, KS94]. PDE [Kny92a]. pencil [Kny83]. Pennsylvania [KX95]. periodic [BK91a, BK91b, BK94]. Physics [LBA^{+}84]. Preconditioned [BK95, KS89, Kny91, KS93b, KS94]. priori [Kny86b]. problem [Kny87a, Kny87b, KS91, KS93b, KS93a, KS94]. Problems [LBA^{+}84, BK90, Kny86a, KS89, Kny91]. Proceedings [KX95, BdG92]. properties [BK91b, BK94].

quotient [KS93a].

rate [Kny87a, KS88, KS91]. Rayleigh [Kny86b, KS93a]. ring [Kny92b]. Ritz [Kny86b, Kny94].

Science [KX95]. Seventh [KX95]. several [KL83]. Sharp [Kny86b]. sign [Kny86b]. simultaneous [KL83]. solution [Kny92a]. Solving [LBA^{+}84, BK90, BKK91, BK92, KS89]. Some [Kny83, LBA^{+}84, Kny87b]. spaces [BKE94]. spectrum [Kny83]. State [KX95]. Stationary [LBA^{+}84]. steepest [KS88, KS91]. step [Kny83]. Stokes [BK92]. strongly [Kny92a]. structure [BK91a, BK91b, BK94]. Subspace [BK95, KS89, Kny91, Kny92b, KS93b, KS94]. symmetric [Kny87a, Kny87b, KS91, KS93b, KS93a, KS94]. Symposium [BdG92, GKM^{+}91]. systems [KS89].

Temple [KLS90]. Temple-Lehmann [KLS90]. two [Kny83]. two-step [Kny83]. type [BKE94, KS93b, KS94].

University [KX95].

Variational [KS93a]. varying [BKK91, Kny92a]. vectors [Kny94]. version [Kny92a].

which [BK91b]. without [Kny86b].

References

Beauwens:1992:IML

[BdG92] R. Beauwens and P. de Groen, editors. Iterative Methods in Linear Algebra: proceedings of the IMACS International Symposium on Iterative Methods in Linear Algebra, Brussels, Belgium, 2–4 April, 1991. Elsevier Science Publishers, Amsterdam, The Netherlands, 1992. ISBN 0-444-89248-6. LCCN QA184 .I44 1991. Proceedings IMACS Symp. Iterative Methods in Linear Algebra, Brussels, 1991.

Bakhvalov:1990:NIA

[BK90] N. S. Bakhvalov and A. V.

Knyazev. A new iterative algorithm for solving problems of the fictitious flow method for elliptic equations. Soviet Math. Doklady, 41(3):481–485, 1990.

Bakhvalov:1991:ECA

[BK91a] N. S. Bakhvalov and A. V.

Knyazev. Efficient computation of averaged characteristics of composites of a periodic structure of essentially different materials. Soviet Math. Doklady, 42(1):57–62, 1991.

Bakhvalov:1991:MEC

[BK91b] N. S. Bakhvalov and A. V.

Knyazev. Methods of effective computation of homogenized properties for the composites with a periodic structure which consist of essentially different components. In Gury I. Marchuk, editor, Computational Processes and Systems, No. 8, pages 52–94. Nauka, Moscow, Russia, 1991. In Russian.

Bakhvalov:1992:EIM

[BK92] N. S. Bakhvalov and A. V. Knyazev. An efficient iterative method for solving the Lamé equations for almost incompressible media and Stokes’ equations. Soviet Math. Doklady, 44(1):4–9, 1992.

Bakhvalov:1994:FDM

[BK94] N. S. Bakhvalov and A. V. Knyazev. Fictitious domain methods and computation of homogenized properties of composites with a periodic structure of essentially different components. In Marchuk [Mar94], pages 221–276. ISBN 0-8493-8947-X. LCCN QA297 .N8619 1994.

Bakhvalov:1995:PIM

[BK95] N. S. Bakhvalov and A. V. Knyazev. Preconditioned iterative methods in a subspace. In Keyes and Xu [KX95], page 000. ISBN 0-8218-5171-3. LCCN QA402.2 .I55 1993.

Bakhvalov:1994:IKT

[BKE94] N. S. Bakhvalov, A. V. Knyazev, and M. E. Eglit. An inequality of the Korn type and orthogonal decompositions in spaces of matrices. Russian Acad. Sci. Math. Doklady, 48(1):127–129, 1994.

Bakhvalov:1991:IMSa

[BKK91] N. S. Bakhvalov, A. V. Knyazev, and G. M. Kobel’kov. Iterative methods for solving equations with highly varying coefficients. In Glowinski et al. [GKM^{+}91], pages 197–205. ISBN 0-89871-278-5. LCCN QA402.2 .I57 199.

Gyakonov:1982:GIM

[DK82] E. G. D’yakonov and A. V.

Knyazev. Group iterative method for finding lower-order eigenvalues. Moscow University, Ser. 15, Computational Math. and Cybernetics, 2:32–40, 1982.

Gyakonov:1992:IMF

[DK92] E. G. D’yakonov and A. V.

Knyazev. On an iterative method for finding lower eigenvalues. Russian J. of Numerical Analysis and Math. Modelling, 7(6):473– 486, 1992.

Glowinski:1991:FIS

[GKM^{+}91] Roland Glowinski, Yuri A.

Kuznetsov, Gérard A. Meurant, Jacques Périaux, and Olof Widlund, editors. Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations. SIAM, Philadelphia, PA, USA, 1991. ISBN 0-89871-278-5. LCCN QA402.2 .I57 199.

Knyazev:1983:ECA

[KL83] A. V. Knyazev and V. I. Lebedev. Estimates for convergence and analysis of the optimality of iterative methods for the simultaneous computation of several eigenvectors. In Computational methods of linear algebra, pages 94–114. Dept. Numerical Math. USSR Academy of Sciences, Moscow, 1983. In Russian.

Knyazev:1990:TLM

[KLS90] A. V. Knyazev, V. I. Lebedev, and A. L. Skorokhodov. The Temple-Lehmann methods in iterative algorithms. Soviet J. Numerical Analysis and Math. Modelling, 5 (4):265–273, 1990.

Knyazev:1983:STS

[Kny83] A. V. Knyazev. Some two-step methods for finding the boundaries of the spectrum of a linear matrix pencil. Technical Report 3749/16, Kurchatov’s Institute of Atomic Energy, Moscow, 1983. In Russian.

Knyazev:1985:CEE

[Kny85] A. V. Knyazev. Computation of eigenvalues and eigenvectors (algorithms and error estimates). PhD thesis, Dept. Numerical Math. USSR Academy of Sciences, Moscow, 1985. In Russian.

Knyazev:1986:CEE

[Kny86a] A. V. Knyazev. Computation of eigenvalues and eigenvectors for mesh problems: algorithms and error estimates. Dept. Numerical Math. USSR Academy of Sciences, Moscow, 1986. In Russian.

Knyazev:1986:SPE

[Kny86b] A. V. Knyazev. Sharp a priori error estimates of the Rayleigh–Ritz method without assumptions of fixed sign or compactness. Math. Notes, 38(5–6):998–1002, 1986.

Knyazev:1987:CRE

[Kny87a] A. V. Knyazev. Convergence rate estimates for iterative methods for mesh symmetric eigenvalue problem. Soviet J. Numerical Analysis and Math. Modelling, 2(5): 371–396, 1987.

Knyazev:1987:MDS

[Kny87b] A. V. Knyazev. Methods for the derivation of some estimates in a symmetric eigenvalue problem. In Gury I. Marchuk, editor, Computational Processes and Systems, No. 5, pages 164–173. Nauka, Moscow, Russia, 1987. In Russian.

Knyazev:1991:PCG

[Kny91] A. V. Knyazev. A preconditioned conjugate gradient method for eigenvalue problems and its implementation in a subspace. In Eigenwertaufgaben in Natur- und Ingenieurwissenschaften und ihre numerische Behandlung, Oberwolfach, 1990, volume 96 of International Series Numerical Mathematics, pages 143–154. Birkhäuser Verlag, Basel, 1991.

Knyazev:1992:ISP

[Kny92a] A. V. Knyazev. Iterative solution of PDE with strongly varying coefficients: algebraic version. In Beauwens and de Groen [BdG92], pages 85–89. ISBN 0-444-89248-6. LCCN QA184 .I44 1991. Proceedings IMACS Symp. Iterative Methods in Linear Algebra, Brussels, 1991.

Knyazev:1992:PAS

[Kny92b] A. V. Knyazev. A parallel algorithm of subspace iterations and its implementation on a multiprocessor with ring architecture. Russian J. Numerical Analysis and Math. Modelling, 7(1):55–61, 1992.

Knyazev:1994:NER

[Kny94] A. V. Knyazev. New estimates for Ritz vectors. Technical Report 677, CIMS NYU, New York, 1994.

Knyazev:1988:CRS

[KS88] A. V. Knyazev and A. L. Skorokhodov. On the convergence rate of the steepest descent method in euclidean norm. USSR J. Comput. Math. and Math. Physics, 28(5):195–196, 1988.

Knyazev:1989:PIMa

[KS89] A. V. Knyazev and A. L. Skorokhodov. Preconditioned iterative methods in subspace for solving linear systems with indefinite coefficient matrices and eigenvalue problems. Soviet J. Numerical Analysis and Math. Modelling, 4 (4):283–310, 1989.

Knyazev:1991:EEC

[KS91] A. V. Knyazev and A. L. Skorokhodov. On exact estimates of the convergence rate of the steepest ascent method in the symmetric eigenvalue problem. Linear Algebra and Applications, 154–156: 245–257, 1991.

Knyazev:1993:VRQ

[KS93a] A. V. Knyazev and I. A. Sharapov. Variational Rayleigh quotient iteration methods for symmetric eigenvalue problem. East-West J. of Numerical Mathematics, 1(2):121–128, 1993.

Knyazev:1993:PGT

[KS93b] A. V. Knyazev and A. L. Skorokhodov. The preconditioned gradient-type iterative methods in a subspace for partial generalized symmetric eigenvalue problem. Soviet Math. Doklady, 45(2): 474–478, 1993.

Knyazev:1994:PGT

[KS94] A. V. Knyazev and A. L. Skorokhodov. The preconditioned gradient-type iterative methods in a subspace for partial generalized symmetric eigenvalue problem. SIAM J. Numerical Analysis, 31(4):1226, 1994.

Keyes:1995:DDM

[KX95] David E. Keyes and Jinchao Xu, editors. Domain Decomposition Methods in Science and Engineering: Proceedings of the Seventh International Conference on Domain Decomposition, October 27– 30, 1993, The Pennsylvania State University, Contemporary Mathematics. Amer. Math. Soc., Providence, RI, USA, 1995. ISBN 0-8218-5171-3. LCCN QA402.2 .I55 1993.

Lebedev:1984:PAS

[LBA^{+}84] V. I. Lebedev, N. S. Bakhvalov, V. I. Agoshkov, O. V. Baburin, A. V. Knyazev, and V. P. Shutyaev. Parallel Algorithms for Solving Some Stationary Problems of Mathemetical Physics. Dept. Numerical Math. USSR Academy of Sciences, Moscow, 1984. Foreword by G. I. Marchuk. In Russian.

Marchuk:1994:NMA

[Mar94] Guri I. Marchuk, editor. Numerical Methods and Applications. CRC Press, 2000 Corporate Blvd., Boca Raton, FL 33431, USA, 1994. ISBN 0-8493-8947-X. x + 272 pp. LCCN QA297 .N8619 1994.