Edit Profile (opens in new tab) Tichý, Petr Compute Distance To: Compute Author ID: tichy.petr Published as: Tichý, Petr; Tichý, P. Homepage: http://www.karlin.mff.cuni.cz/~ptichy/ External Links: ORCID · dblp Documents Indexed: 28 Publications since 1998 2 Contributions as Editor Reviewing Activity: 8 Reviews Co-Authors: 24 Co-Authors with 30 Joint Publications 533 Co-Co-Authors all top 5 Co-Authors 0 single-authored 12 Liesen, Jörg 6 Strakoš, Zdeněk 5 Faber, Vance 4 Meurant, Gérard A. 2 Echeverria, Carlos 2 Jaros, Jiri 2 Kozubek, Tomas 2 Šístek, Jakub 2 Sysala, Stanislav 1 Arbenz, Peter 1 Blaheta, Radim 1 Carson, Erin Claire 1 Čermák, Martin 1 Dolejší, Vít 1 Hnětynková, Iveta 1 Lukáš, Dalibor 1 O’Leary, Dianne P. 1 Papež, Jan 1 Říha, Lubomír 1 Rozložník, Miroslav 1 Šimonová, Dorota 1 Szyld, Daniel B. 1 Tůma, Miroslav 1 Zítko, Jan all top 5 Serials 7 ETNA. Electronic Transactions on Numerical Analysis 5 Numerical Algorithms 3 SIAM Journal on Matrix Analysis and Applications 3 Applications of Mathematics 2 BIT 2 SIAM Journal on Scientific Computing 2 Lecture Notes in Computer Science 1 Numerische Mathematik 1 SIAM Journal on Numerical Analysis 1 Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik 1 Journal of Scientific Computing 1 Linear Algebra and its Applications 1 PAMM. Proceedings in Applied Mathematics and Mechanics all top 5 Fields 28 Numerical analysis (65-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 4 General and overarching topics; collections (00-XX) 3 Approximations and expansions (41-XX) 2 Operations research, mathematical programming (90-XX) 1 Partial differential equations (35-XX) 1 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 21 Publications have been cited 150 times in 105 Documents Cited by ▼ Year ▼ On error estimation in the conjugate gradient method and why it works in finite precision computations. Zbl 1026.65027Strakoš, Zdeněk; Tichý, Petr 30 2002 Convergence analysis of Krylov subspace methods. Zbl 1071.65041Liesen, Jörg; Tichý, Petr 19 2004 Error estimation in preconditioned conjugate gradients. Zbl 1095.65029Strakoš, Zdeněk; Tichý, Petr 17 2005 The worst-case GMRES for normal matrices. Zbl 1053.65021Liesen, Jörg; Tichý, Petr 12 2004 On computing quadrature-based bounds for the \(A\)-norm of the error in conjugate gradients. Zbl 1261.65034Meurant, Gérard; Tichý, Petr 12 2013 On sensitivity of Gauss-Christoffel quadrature. Zbl 1117.41023O’Leary, Dianne P.; Strakoš, Zdeněk; Tichý, Petr 9 2007 On efficient numerical approximation of the bilinear form \(c^*A^{-1}b\). Zbl 1227.65033Strakoš, Zdeněk; Tichý, Petr 8 2011 The Faber-Manteuffel theorem for linear operators. Zbl 1170.65024Faber, V.; Liesen, J.; Tichý, P. 6 2008 Approximating the extreme Ritz values and upper bounds for the \(A\)-norm of the error in CG. Zbl 1436.65033Meurant, Gérard; Tichý, Petr 5 2019 On best approximations of polynomials in matrices in the matrix 2-norm. Zbl 1190.41011Liesen, Jörg; Tichý, Petr 5 2009 On worst-case GMRES, ideal GMRES, and the polynomial numerical hull of a Jordan block. Zbl 1171.65373Tichý, Petr; Liesen, Jörg; Faber, Vance 5 2007 The numerical stability analysis of pipelined conjugate gradient methods: historical context and methodology. Zbl 1416.65080Carson, Erin C.; Rozložník, Miroslav; Strakoš, Zdeněk; Tichý, Petr; Tuma, Miroslav 4 2018 Convergence of the multiplicative Schwarz method for singularly perturbed convection-diffusion problems discretized on a Shishkin mesh. Zbl 1390.15072Echeverría, Carlos; Liesen, Jörg; Szyld, Daniel B.; Tichý, Petr 3 2018 On orthogonal reduction to Hessenberg form with small bandwidth. Zbl 1180.65051Faber, V.; Liesen, J.; Tichý, P. 3 2009 On efficient numerical solution of linear algebraic systems arising in goal-oriented error estimates. Zbl 1435.65188Dolejší, Vít; Tichý, Petr 2 2020 On the worst-case convergence of MR and CG for symmetric positive definite tridiagonal Toeplitz matrices. Zbl 1119.65320Liesen, Jörg; Tichý, Petr 2 2005 Properties of worst-case GMRES. Zbl 1291.65096Faber, Vance; Liesen, Jörg; Tichý, Petr 2 2013 Erratum to: “On computing quadrature-based bounds for the A-norm of the error in conjugate gradients”. Zbl 1298.65062Meurant, Gérard; Tichý, Petr 2 2014 On Chebyshev polynomials of matrices. Zbl 1206.41004Faber, Vance; Liesen, Jörg; Tichý, Petr 2 2010 On estimation of the \(A\)-norm of the error in CG and PCG. Zbl 1354.90173Strakoš, Zdeněk; Tichý, Petr 1 2003 Accurate error estimation in CG. Zbl 1490.65056Meurant, Gérard; Papež, Jan; Tichý, Petr 1 2021 Accurate error estimation in CG. Zbl 1490.65056Meurant, Gérard; Papež, Jan; Tichý, Petr 1 2021 On efficient numerical solution of linear algebraic systems arising in goal-oriented error estimates. Zbl 1435.65188Dolejší, Vít; Tichý, Petr 2 2020 Approximating the extreme Ritz values and upper bounds for the \(A\)-norm of the error in CG. Zbl 1436.65033Meurant, Gérard; Tichý, Petr 5 2019 The numerical stability analysis of pipelined conjugate gradient methods: historical context and methodology. Zbl 1416.65080Carson, Erin C.; Rozložník, Miroslav; Strakoš, Zdeněk; Tichý, Petr; Tuma, Miroslav 4 2018 Convergence of the multiplicative Schwarz method for singularly perturbed convection-diffusion problems discretized on a Shishkin mesh. Zbl 1390.15072Echeverría, Carlos; Liesen, Jörg; Szyld, Daniel B.; Tichý, Petr 3 2018 Erratum to: “On computing quadrature-based bounds for the A-norm of the error in conjugate gradients”. Zbl 1298.65062Meurant, Gérard; Tichý, Petr 2 2014 On computing quadrature-based bounds for the \(A\)-norm of the error in conjugate gradients. Zbl 1261.65034Meurant, Gérard; Tichý, Petr 12 2013 Properties of worst-case GMRES. Zbl 1291.65096Faber, Vance; Liesen, Jörg; Tichý, Petr 2 2013 On efficient numerical approximation of the bilinear form \(c^*A^{-1}b\). Zbl 1227.65033Strakoš, Zdeněk; Tichý, Petr 8 2011 On Chebyshev polynomials of matrices. Zbl 1206.41004Faber, Vance; Liesen, Jörg; Tichý, Petr 2 2010 On best approximations of polynomials in matrices in the matrix 2-norm. Zbl 1190.41011Liesen, Jörg; Tichý, Petr 5 2009 On orthogonal reduction to Hessenberg form with small bandwidth. Zbl 1180.65051Faber, V.; Liesen, J.; Tichý, P. 3 2009 The Faber-Manteuffel theorem for linear operators. Zbl 1170.65024Faber, V.; Liesen, J.; Tichý, P. 6 2008 On sensitivity of Gauss-Christoffel quadrature. Zbl 1117.41023O’Leary, Dianne P.; Strakoš, Zdeněk; Tichý, Petr 9 2007 On worst-case GMRES, ideal GMRES, and the polynomial numerical hull of a Jordan block. Zbl 1171.65373Tichý, Petr; Liesen, Jörg; Faber, Vance 5 2007 Error estimation in preconditioned conjugate gradients. Zbl 1095.65029Strakoš, Zdeněk; Tichý, Petr 17 2005 On the worst-case convergence of MR and CG for symmetric positive definite tridiagonal Toeplitz matrices. Zbl 1119.65320Liesen, Jörg; Tichý, Petr 2 2005 Convergence analysis of Krylov subspace methods. Zbl 1071.65041Liesen, Jörg; Tichý, Petr 19 2004 The worst-case GMRES for normal matrices. Zbl 1053.65021Liesen, Jörg; Tichý, Petr 12 2004 On estimation of the \(A\)-norm of the error in CG and PCG. Zbl 1354.90173Strakoš, Zdeněk; Tichý, Petr 1 2003 On error estimation in the conjugate gradient method and why it works in finite precision computations. Zbl 1026.65027Strakoš, Zdeněk; Tichý, Petr 30 2002 all cited Publications top 5 cited Publications all top 5 Cited by 190 Authors 11 Meurant, Gérard A. 11 Strakoš, Zdeněk 11 Tichý, Petr 5 Liesen, Jörg 4 Carson, Erin Claire 4 Li, Rencang 4 Papež, Jan 3 Arioli, Mario 3 Chen, Tyler 3 Dolejší, Vít 3 Duintjer Tebbens, Jurjen 3 Greenbaum, Anne 3 Vohralík, Martin 2 Bevilacqua, Roberto 2 Del Corso, Gianna M. 2 Higham, Nicholas J. 2 Kuchta, Miroslav 2 Mardal, Kent-Andre 2 Morgan, Ronald B. 2 Plešinger, Martin 2 Sadok, Hassane 2 Salemi, Abbas 2 Simoncini, Valeria 2 Szyld, Daniel B. 2 Vandebril, Raf 2 Wathen, Andrew John 1 Agullo, Emmanuel 1 Ahmad, Mian Ilyas 1 Aliaga, José Ignacio 1 Atroshchenko, Elena 1 Axelsson, Axel Owe Holger 1 Badcock, Kenneth J. 1 Bak, Soyoon 1 Bartoš, Ondřej 1 Bastian, Peter 1 Beckermann, Bernhard 1 Bollhöfer, Matthias 1 Boon, Wietse M. 1 Bouyouli, R. 1 Bramas, Bérenger 1 Bujurke, Nagendrappa M. 1 Chae, Minwoo 1 Chen, Caihua 1 Cockayne, Jon 1 Constantine, Paul G. 1 Cools, Siegfried 1 Cui, Tiangang 1 Dahmen, Wolfgang A. 1 Danilov, Dmitry I. 1 Dessole, Monica 1 Diaz Cortés, Gabriela Berenice 1 Du, Lei 1 Echeverria, Carlos 1 Eisenträger, Sascha 1 Embree, Mark 1 Eshghi, Nasim 1 Estrin, Ron 1 Faber, Vance 1 Fika, Paraskevi 1 Futamura, Yasunori 1 Gaaf, Sarah W. 1 Galkowski, Jeffrey 1 García-Ardila, Juan Carlos 1 Gemignani, Luca 1 Georgiev, Krassimir 1 Gergelits, Tomáš 1 Giraud, Luc 1 Gmati, Nabil 1 Götschel, Sebastian 1 Gratton, Serge 1 Grover, Priyanka 1 Guo, Shaoyan 1 Gutknecht, Martin H. 1 Hallman, Eric 1 Hao, Shoulin 1 Hassan, Muhammad 1 Hnětynková, Iveta 1 Hornkjøl, Martin 1 Ipsen, Ilse C. F. 1 Jansen, Jan-Dirk 1 Jeon, Yonghyeon 1 Jia, Zhigang 1 Kantli, Mounesha H. 1 Karami, Saeed 1 Karátson, János 1 Kressner, Daniel 1 Kyanfar, Faranges 1 Ladecký, Martin 1 Li, Shishun 1 Ling, Sitao 1 Liu, Hexuan 1 Liu, Yong-Jin 1 Loghin, Daniel 1 Mach, Thomas 1 MacLachlan, Scott P. 1 Madden, Niall 1 Magnus, Jan R. 1 Makvandi, Resam 1 Mantica, Giorgio 1 Marcellán Español, Francisco ...and 90 more Authors all top 5 Cited in 42 Serials 14 Numerical Algorithms 11 Linear Algebra and its Applications 8 SIAM Journal on Scientific Computing 7 SIAM Journal on Matrix Analysis and Applications 5 BIT 4 Computers & Mathematics with Applications 4 Numerische Mathematik 4 Numerical Linear Algebra with Applications 4 ETNA. Electronic Transactions on Numerical Analysis 3 Journal of Computational and Applied Mathematics 3 Applied Numerical Mathematics 2 Journal of Computational Physics 2 Journal of Mathematical Analysis and Applications 2 Mathematics of Computation 2 Applied Mathematics and Computation 2 Journal of Scientific Computing 1 Computers and Fluids 1 Computer Physics Communications 1 Linear and Multilinear Algebra 1 Results in Mathematics 1 Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik 1 Parallel Computing 1 Applied Mathematics Letters 1 Computational Mathematics and Modeling 1 Applications of Mathematics 1 International Journal of Computer Mathematics 1 Computational Statistics and Data Analysis 1 Mathematical Programming. Series A. Series B 1 Computational Optimization and Applications 1 Advances in Computational Mathematics 1 ELA. The Electronic Journal of Linear Algebra 1 Journal of Mathematical Chemistry 1 Computational Geosciences 1 Journal of Machine Learning Research (JMLR) 1 Central European Journal of Mathematics 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 GAMM-Mitteilungen 1 Communications in Computational Physics 1 SIAM Journal on Imaging Sciences 1 Advances in Numerical Analysis 1 Journal of the Operations Research Society of China 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences all top 5 Cited in 25 Fields 95 Numerical analysis (65-XX) 25 Linear and multilinear algebra; matrix theory (15-XX) 8 Partial differential equations (35-XX) 8 Fluid mechanics (76-XX) 6 Approximations and expansions (41-XX) 4 Computer science (68-XX) 3 Statistics (62-XX) 3 Mechanics of deformable solids (74-XX) 3 Operations research, mathematical programming (90-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Operator theory (47-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Geophysics (86-XX) 2 Information and communication theory, circuits (94-XX) 1 Functions of a complex variable (30-XX) 1 Special functions (33-XX) 1 Sequences, series, summability (40-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 General topology (54-XX) 1 Optics, electromagnetic theory (78-XX) 1 Quantum theory (81-XX) 1 Astronomy and astrophysics (85-XX) 1 Systems theory; control (93-XX) Citations by Year