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Byers, Ralph

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 Author ID: byers.ralph Published as: Byers, Ralph; Byers, R.
 Documents Indexed: 44 Publications since 1984 Biographic References: 1 Publication
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Co-Authors

 9 single-authored 17 Mehrmann, Volker 12 Benner, Peter 7 Xu, Hongguo 5 Bunse-Gerstner, Angelika 3 Nichols, Nancy K. 2 Alam, Rafikul 2 Braman, Karen 2 He, Chunyang 2 Kressner, Daniel 2 Mathias, Roy 2 Nash, Stephen G. 2 Quintana-Ortí, Enrique S. 1 Barth, Eric 1 Bora, Shreemayee 1 Faßbender, Heike 1 Geerts, Ton 1 Harris, Bernard J. 1 Hernández, Vicente G. 1 Kunkel, Peter 1 Losse, Philip 1 Man Kam Kwong 1 Mayo, Rafael 1 Overton, Michael L. 1 Quintana-Ortí, Gregorio 1 Safique Ahmad, Sk. 1 Watkins, David S.
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Serials

 9 SIAM Journal on Matrix Analysis and Applications 7 Linear Algebra and its Applications 3 IEEE Transactions on Automatic Control 3 Numerische Mathematik 2 SIAM Journal on Control and Optimization 2 SIAM Journal on Scientific and Statistical Computing 2 ETNA. Electronic Transactions on Numerical Analysis 1 International Journal of Control 1 ACM Transactions on Mathematical Software 1 Automatica 1 BIT 1 Journal of Differential Equations 1 SIAM Journal on Algebraic and Discrete Methods 1 Parallel Computing 1 Journal of Parallel and Distributed Computing 1 Numerical Linear Algebra with Applications 1 Methods of Operations Research
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Fields

 34 Numerical analysis (65-XX) 23 Linear and multilinear algebra; matrix theory (15-XX) 19 Systems theory; control (93-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 2 Computer science (68-XX) 1 Ordinary differential equations (34-XX) 1 Mechanics of deformable solids (74-XX) 1 Operations research, mathematical programming (90-XX)

Citations contained in zbMATH Open

43 Publications have been cited 740 times in 561 Documents Cited by Year
A bisection method for measuring the distance of a stable matrix to the unstable matrices. Zbl 0658.65044
Byers, Ralph
1988
Weighted means and oscillation conditions for second order matrix differential equations. Zbl 0609.34042
Byers, Ralph; Harris, B. J.; Man Kam Kwong
1986
Numerical computation of an analytic singular value decomposition of a matrix valued function. Zbl 0743.65035
Bunse-Gerstner, Angelika; Byers, Ralph; Mehrmann, Volker; Nichols, Nancy K.
1991
Solving the algebraic Riccati equation with the matrix sign function. Zbl 0611.65027
Byers, Ralph
1987
A chart of numerical methods for structured eigenvalue problems. Zbl 0757.65040
Bunse-Gerstner, Angelika; Byers, Ralph; Mehrmann, Volker
1992
A Hamiltonian QR algorithm. Zbl 0611.65026
Byers, Ralph
1986
On the stability radius of a generalized state-space system. Zbl 0783.65056
Byers, Ralph; Nichols, N. K.
1993
Numerical computation of deflating subspaces of skew-Hamiltonian/Hamiltonian pencils. Zbl 1035.49022
Benner, Peter; Byers, Ralph; Mehrmann, Volker; Xu, Hongguo
2002
A quaternion QR-algorithm. Zbl 0681.65024
Bunse-Gerstner, Angelika; Byers, Ralph; Mehrmann, Volker
1989
Structured condition numbers for invariant subspaces. Zbl 1116.65052
Byers, Ralph; Kressner, Daniel
2006
An exact line search method for solving generalized continuous-time algebraic Riccati equations. Zbl 0908.93026
Benner, Peter; Byers, Ralph
1998
The multishift QR algorithm. I: Maintaining well-focused shifts and level 3 performance. Zbl 1017.65031
Braman, Karen; Byers, Ralph; Mathias, Roy
2002
The multishift QR algorithm. II: Aggressive early deflation. Zbl 1017.65032
Braman, Karen; Byers, Ralph; Mathias, Roy
2002
Feedback design for regularizing descriptor systems. Zbl 0944.65082
Bunse-Gerstner, Angelika; Byers, Ralph; Mehrmann, Volker; Nichols, Nancy K.
1999
Cholesky-like factorizations of skew-symmetric matrices. Zbl 0963.65033
Benner, Peter; Byers, Ralph; Fassbender, Heike; Mehrmann, Volker; Watkins, David
2000
Approaches to robust pole assignment. Zbl 0666.93042
Byers, Ralph; Nash, Stephen G.
1989
A structured staircase algorithm for skew-symmetric/symmetric pencils. Zbl 1113.65065
Byers, Ralph; Mehrmann, Volker; Xu, Hongguo
2007
A robust numerical method for the $$\gamma$$-iteration in $$H_{\infty}$$ control. Zbl 1124.93022
Benner, Peter; Byers, Ralph; Mehrmann, Volker; Xu, Hongguo
2007
Evaluating products of matrix pencils and collapsing matrix products. Zbl 1055.65053
Benner, Peter; Byers, Ralph
2001
Numerical methods for simultaneous diagonalization. Zbl 0786.65030
Bunse-Gerstner, Angelika; Byers, Ralph; Mehrmann, Volker
1993
Regularization of linear descriptor systems with variable coefficients. Zbl 0895.93026
Byers, Ralph; Kunkel, Peter; Mehrmann, Volker
1997
Descriptor systems without controllability at infinity. Zbl 0871.93021
Byers, Ralph; Geerts, Ton; Mehrmann, Volker
1997
The matrix sign function method and the computation of invariant subspaces. Zbl 0874.65031
Byers, Ralph; He, Chunyang; Mehrmann, Volker
1997
An arithmetic for matrix pencils: theory and new algorithms. Zbl 1101.65046
Benner, Peter; Byers, Ralph
2006
Trimmed linearizations for structured matrix polynomials. Zbl 1155.65026
Byers, Ralph; Mehrmann, Volker; Xu, Hongguo
2008
Where is the nearest non-regular pencil? Zbl 0935.15013
Byers, Ralph; He, Chunyang; Mehrmann, Volker
1998
On the singular “vectors” of the Lyapunov operator. Zbl 0633.65042
Byers, Ralph; Nash, Stephen
1987
A LINPACK-style condition estimator for the equation $$AX-XB^ T=C$$. Zbl 0544.65027
Byers, Ralph
1984
On the condition of a complex eigenvalue under real perturbations. Zbl 1071.15004
Byers, R.; Kressner, D.
2004
A new scaling for Newton’s iteration for the polar decomposition and its backward stability. Zbl 1170.65019
Byers, Ralph; Xu, Hongguo
2008
On pseudospectra, critical points, and multiple eigenvalues of matrix pencils. Zbl 1206.65137
Ahmad, Sk. Safique; Alam, Rafikul; Byers, Ralph
2010
Characterization and construction of the nearest defective matrix via coalescence of pseudospectral components. Zbl 1228.65062
Alam, Rafikul; Bora, Shreemayee; Byers, Ralph; Overton, Michael L.
2011
Detecting nearly uncontrollable pairs. Zbl 0722.93010
Byers, Ralph
1990
Robust formulas for $$H_{\infty }$$ optimal controllers. Zbl 1252.93047
Benner, Peter; Byers, Ralph; Losse, Philip; Mehrmann, Volker; Xu, Hongguo
2011
Numerical methods for linear quadratic and $$H_\infty$$ control problems. Zbl 0928.93017
Benner, Peter; Byers, Ralph; Mehrmann, Volker; Xu, Hongguo
1999
Solving algebraic Riccati equations on parallel computers using Newton’s method with exact line search. Zbl 0949.65041
Benner, P.; Byers, R.; Quintana-Ortí, E. S.; Quintana-Ortí, G.
2000
Parallel algorithms for LQ optimal control of discrete-time periodic linear systems. Zbl 1008.93035
Benner, Peter; Byers, Ralph; Mayo, Rafael; Quintana-Ortí, Enrique S.; Hernández, Vicente
2002
The descriptor controllability radius. Zbl 0925.93084
Byers, Ralph
1994
A Hamiltonian-Jacobi algorithm. Zbl 0706.65066
Byers, Ralph
1990
Numerical condition of the algebraic Riccati equation. Zbl 0579.65037
Byers, Ralph
1985
Algorithm 800. Fortran 77 subroutines for computing the eigenvalues of Hamiltonian matrices. I: The square-reduced method. Zbl 1137.65338
Benner, Peter; Byers, Ralph; Barth, Eric
2000
Step size control for Newton’s method applied to algebraic Riccati equations. Zbl 0819.65078
Benner, Peter; Byers, Ralph
1994
Symmetric updating of the solution of the algebraic Riccati equation. Zbl 0664.93024
Byers, Ralph; Mehrmann, Volker
1986
Characterization and construction of the nearest defective matrix via coalescence of pseudospectral components. Zbl 1228.65062
Alam, Rafikul; Bora, Shreemayee; Byers, Ralph; Overton, Michael L.
2011
Robust formulas for $$H_{\infty }$$ optimal controllers. Zbl 1252.93047
Benner, Peter; Byers, Ralph; Losse, Philip; Mehrmann, Volker; Xu, Hongguo
2011
On pseudospectra, critical points, and multiple eigenvalues of matrix pencils. Zbl 1206.65137
Ahmad, Sk. Safique; Alam, Rafikul; Byers, Ralph
2010
Trimmed linearizations for structured matrix polynomials. Zbl 1155.65026
Byers, Ralph; Mehrmann, Volker; Xu, Hongguo
2008
A new scaling for Newton’s iteration for the polar decomposition and its backward stability. Zbl 1170.65019
Byers, Ralph; Xu, Hongguo
2008
A structured staircase algorithm for skew-symmetric/symmetric pencils. Zbl 1113.65065
Byers, Ralph; Mehrmann, Volker; Xu, Hongguo
2007
A robust numerical method for the $$\gamma$$-iteration in $$H_{\infty}$$ control. Zbl 1124.93022
Benner, Peter; Byers, Ralph; Mehrmann, Volker; Xu, Hongguo
2007
Structured condition numbers for invariant subspaces. Zbl 1116.65052
Byers, Ralph; Kressner, Daniel
2006
An arithmetic for matrix pencils: theory and new algorithms. Zbl 1101.65046
Benner, Peter; Byers, Ralph
2006
On the condition of a complex eigenvalue under real perturbations. Zbl 1071.15004
Byers, R.; Kressner, D.
2004
Numerical computation of deflating subspaces of skew-Hamiltonian/Hamiltonian pencils. Zbl 1035.49022
Benner, Peter; Byers, Ralph; Mehrmann, Volker; Xu, Hongguo
2002
The multishift QR algorithm. I: Maintaining well-focused shifts and level 3 performance. Zbl 1017.65031
Braman, Karen; Byers, Ralph; Mathias, Roy
2002
The multishift QR algorithm. II: Aggressive early deflation. Zbl 1017.65032
Braman, Karen; Byers, Ralph; Mathias, Roy
2002
Parallel algorithms for LQ optimal control of discrete-time periodic linear systems. Zbl 1008.93035
Benner, Peter; Byers, Ralph; Mayo, Rafael; Quintana-Ortí, Enrique S.; Hernández, Vicente
2002
Evaluating products of matrix pencils and collapsing matrix products. Zbl 1055.65053
Benner, Peter; Byers, Ralph
2001
Cholesky-like factorizations of skew-symmetric matrices. Zbl 0963.65033
Benner, Peter; Byers, Ralph; Fassbender, Heike; Mehrmann, Volker; Watkins, David
2000
Solving algebraic Riccati equations on parallel computers using Newton’s method with exact line search. Zbl 0949.65041
Benner, P.; Byers, R.; Quintana-Ortí, E. S.; Quintana-Ortí, G.
2000
Algorithm 800. Fortran 77 subroutines for computing the eigenvalues of Hamiltonian matrices. I: The square-reduced method. Zbl 1137.65338
Benner, Peter; Byers, Ralph; Barth, Eric
2000
Feedback design for regularizing descriptor systems. Zbl 0944.65082
Bunse-Gerstner, Angelika; Byers, Ralph; Mehrmann, Volker; Nichols, Nancy K.
1999
Numerical methods for linear quadratic and $$H_\infty$$ control problems. Zbl 0928.93017
Benner, Peter; Byers, Ralph; Mehrmann, Volker; Xu, Hongguo
1999
An exact line search method for solving generalized continuous-time algebraic Riccati equations. Zbl 0908.93026
Benner, Peter; Byers, Ralph
1998
Where is the nearest non-regular pencil? Zbl 0935.15013
Byers, Ralph; He, Chunyang; Mehrmann, Volker
1998
Regularization of linear descriptor systems with variable coefficients. Zbl 0895.93026
Byers, Ralph; Kunkel, Peter; Mehrmann, Volker
1997
Descriptor systems without controllability at infinity. Zbl 0871.93021
Byers, Ralph; Geerts, Ton; Mehrmann, Volker
1997
The matrix sign function method and the computation of invariant subspaces. Zbl 0874.65031
Byers, Ralph; He, Chunyang; Mehrmann, Volker
1997
The descriptor controllability radius. Zbl 0925.93084
Byers, Ralph
1994
Step size control for Newton’s method applied to algebraic Riccati equations. Zbl 0819.65078
Benner, Peter; Byers, Ralph
1994
On the stability radius of a generalized state-space system. Zbl 0783.65056
Byers, Ralph; Nichols, N. K.
1993
Numerical methods for simultaneous diagonalization. Zbl 0786.65030
Bunse-Gerstner, Angelika; Byers, Ralph; Mehrmann, Volker
1993
A chart of numerical methods for structured eigenvalue problems. Zbl 0757.65040
Bunse-Gerstner, Angelika; Byers, Ralph; Mehrmann, Volker
1992
Numerical computation of an analytic singular value decomposition of a matrix valued function. Zbl 0743.65035
Bunse-Gerstner, Angelika; Byers, Ralph; Mehrmann, Volker; Nichols, Nancy K.
1991
Detecting nearly uncontrollable pairs. Zbl 0722.93010
Byers, Ralph
1990
A Hamiltonian-Jacobi algorithm. Zbl 0706.65066
Byers, Ralph
1990
A quaternion QR-algorithm. Zbl 0681.65024
Bunse-Gerstner, Angelika; Byers, Ralph; Mehrmann, Volker
1989
Approaches to robust pole assignment. Zbl 0666.93042
Byers, Ralph; Nash, Stephen G.
1989
A bisection method for measuring the distance of a stable matrix to the unstable matrices. Zbl 0658.65044
Byers, Ralph
1988
Solving the algebraic Riccati equation with the matrix sign function. Zbl 0611.65027
Byers, Ralph
1987
On the singular “vectors” of the Lyapunov operator. Zbl 0633.65042
Byers, Ralph; Nash, Stephen
1987
Weighted means and oscillation conditions for second order matrix differential equations. Zbl 0609.34042
Byers, Ralph; Harris, B. J.; Man Kam Kwong
1986
A Hamiltonian QR algorithm. Zbl 0611.65026
Byers, Ralph
1986
Symmetric updating of the solution of the algebraic Riccati equation. Zbl 0664.93024
Byers, Ralph; Mehrmann, Volker
1986
Numerical condition of the algebraic Riccati equation. Zbl 0579.65037
Byers, Ralph
1985
A LINPACK-style condition estimator for the equation $$AX-XB^ T=C$$. Zbl 0544.65027
Byers, Ralph
1984
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Cited by 670 Authors

 45 Mehrmann, Volker 32 Benner, Peter 15 Kressner, Daniel 15 Mehl, Christian 15 Meng, Fanwei 11 Quintana-Ortí, Enrique S. 11 Xu, Hongguo 10 Van Dooren, Paul M. 9 Dopico, Froilán M. 9 Faßbender, Heike 9 Sun, Yuangong 7 Byers, Ralph 7 de Terán, Fernando 7 Kågström, Bo 7 Lin, Wen-Wei 7 Linh, Vu Hoang 7 Mackey, D. Steven 7 Poloni, Federico G. 6 Kononov, Alekseĭ Denisovich 6 Kunkel, Peter 6 Reis, Timo 6 Sharma, Punit 6 Shcheglova, Alla Arkad’evna 6 Stykel, Tatjana 6 Watkins, David S. 5 Alam, Rafikul 5 Chu, Moody T. 5 Diao, Huaian 5 Fan, Hung-Yuan 5 Guglielmi, Nicola 5 Iannazzo, Bruno 5 Jia, Zhigang 5 Noferini, Vanni 5 Noschese, Silvia 5 Petkov, Petko Hr. 5 Quintana-Ortí, Gregorio 5 Rodman, Leiba X. 5 Voigt, Matthias 5 Wei, Yimin 5 Yang, Qigui 5 Zhang, Shao-Liang 4 Chiang, Chun-Yueh 4 Chu, Delin 4 Higham, Nicholas J. 4 Karow, Michael 4 King-wah Chu, Eric 4 Konstantinov, Mikhail Mikhajlov 4 Kostić, Vladimir R. 4 Laub, Alan J. 4 Li, Wen 4 Lu, Linzhang 4 Mackey, Niloufer 4 Mengi, Emre 4 Michiels, Wim 4 Nakatsukasa, Yuji 4 Protasov, Vladimir Yu. 4 Remón, Alfredo 4 Safique Ahmad, Sk. 4 Simoncini, Valeria 4 Sogabe, Tomohiro 4 Soleymani, Fazlollah 4 Stefanovski, Jovan D. 4 Sun, Jiguang 4 Tisseur, Françoise 4 Vandebril, Raf 4 Wei, Musheng 4 Wojtylak, Michał 4 Zheng, Zhaowen 3 Adhikari, Bibhas 3 Baur, Ulrike 3 Bora, Shreemayee 3 Christov, Nicolai D. 3 Chu, E. K.-W. 3 Cvetković, Ljiljana 3 Darouach, Mohamed 3 Dieci, Luca 3 Dmytryshyn, Andrii R. 3 Duan, Guangren 3 Erbe, Lynn Harry 3 Ezzatti, Pablo 3 Freitag, Melina A. 3 Gawlik, Evan S. 3 Gillis, Nicolas 3 He, ZhuoHeng 3 Karlsson, Lars 3 Kenney, Charles S. 3 Khoromskij, Boris N. 3 Kilic, Emrah 3 Li, Hanyu 3 Lin, Matthew M. 3 Malyshev, Alexander N. 3 Mingarelli, Angelo B. 3 Mitchell, Tim 3 Nguyen Huu Du 3 Ran, André C. M. 3 Saak, Jens 3 Sadkane, Miloud 3 Scholz, Lena 3 Schröder, Christian 3 Spence, Alastair ...and 570 more Authors
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Cited in 124 Serials

 115 Linear Algebra and its Applications 35 SIAM Journal on Matrix Analysis and Applications 34 Journal of Computational and Applied Mathematics 23 Applied Mathematics and Computation 21 Automatica 21 Systems & Control Letters 21 Numerical Linear Algebra with Applications 14 Numerische Mathematik 13 International Journal of Control 12 Journal of Mathematical Analysis and Applications 12 BIT 12 MCSS. Mathematics of Control, Signals, and Systems 9 Journal of the Franklin Institute 8 Applied Numerical Mathematics 7 Linear and Multilinear Algebra 7 Numerical Algorithms 6 Computers & Mathematics with Applications 6 SIAM Journal on Scientific Computing 5 Mathematics of Computation 5 Computational and Applied Mathematics 5 ELA. The Electronic Journal of Linear Algebra 5 Mathematical Problems in Engineering 5 East Asian Journal on Applied Mathematics 4 Rocky Mountain Journal of Mathematics 4 Calcolo 4 Journal of Differential Equations 4 Proceedings of the American Mathematical Society 4 Applied Mathematics Letters 3 International Journal of Systems Science 3 ACM Transactions on Mathematical Software 3 Mathematical and Computer Modelling 3 Journal of Scientific Computing 3 Japan Journal of Industrial and Applied Mathematics 3 Automation and Remote Control 3 Journal of Mathematical Sciences (New York) 3 Advances in Applied Clifford Algebras 3 ETNA. Electronic Transactions on Numerical Analysis 3 Acta Numerica 3 Complex Analysis and Operator Theory 2 Computer Methods in Applied Mechanics and Engineering 2 Computer Physics Communications 2 Journal of Optimization Theory and Applications 2 Kybernetika 2 SIAM Journal on Control and Optimization 2 Parallel Computing 2 SIAM Review 2 SIAM Journal on Optimization 2 Applied Mathematics. Series B (English Edition) 2 European Journal of Control 2 Discrete Dynamics in Nature and Society 2 Journal of Interdisciplinary Mathematics 2 PAMM. Proceedings in Applied Mathematics and Mechanics 2 Izvestiya Irkutskogo Gosudarstvennogo Universiteta. Seriya Matematika 2 Nonlinear Analysis. Theory, Methods & Applications 1 Communications in Mathematical Physics 1 International Journal of Engineering Science 1 Journal of Computational Physics 1 Journal of Engineering Mathematics 1 Journal of Mathematical Physics 1 Ukrainian Mathematical Journal 1 Acta Mathematica Vietnamica 1 Annales de l’Institut Fourier 1 Archivum Mathematicum 1 Computing 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 SIAM Journal on Numerical Analysis 1 Transactions of the American Mathematical Society 1 Topology and its Applications 1 Optimal Control Applications & Methods 1 Advances in Applied Mathematics 1 SIAM Journal on Algebraic and Discrete Methods 1 Circuits, Systems, and Signal Processing 1 Applied Mathematics and Mechanics. (English Edition) 1 Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik 1 Computer Aided Geometric Design 1 Journal of Symbolic Computation 1 Constructive Approximation 1 International Journal of Parallel Programming 1 Multidimensional Systems and Signal Processing 1 International Journal of Computer Mathematics 1 Journal of Statistical Computation and Simulation 1 Expositiones Mathematicae 1 Journal of Dynamics and Differential Equations 1 Computational Optimization and Applications 1 Journal of Computer and Systems Sciences International 1 The Journal of Analysis 1 Algebra Colloquium 1 Turkish Journal of Mathematics 1 Advances in Computational Mathematics 1 Journal of Difference Equations and Applications 1 Bernoulli 1 Journal of Vibration and Control 1 Vietnam Journal of Mathematics 1 Abstract and Applied Analysis 1 Optimization Methods & Software 1 Journal of Inequalities and Applications 1 Mathematical Inequalities & Applications 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Mathematical and Computer Modelling of Dynamical Systems 1 Journal of Discrete Mathematical Sciences & Cryptography ...and 24 more Serials
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Cited in 49 Fields

 304 Numerical analysis (65-XX) 280 Linear and multilinear algebra; matrix theory (15-XX) 169 Systems theory; control (93-XX) 89 Ordinary differential equations (34-XX) 33 Calculus of variations and optimal control; optimization (49-XX) 23 Operator theory (47-XX) 17 Dynamical systems and ergodic theory (37-XX) 16 Operations research, mathematical programming (90-XX) 6 Difference and functional equations (39-XX) 6 Mechanics of deformable solids (74-XX) 5 Approximations and expansions (41-XX) 5 Mechanics of particles and systems (70-XX) 4 Combinatorics (05-XX) 4 Number theory (11-XX) 4 Nonassociative rings and algebras (17-XX) 4 Real functions (26-XX) 4 Partial differential equations (35-XX) 4 Functional analysis (46-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Group theory and generalizations (20-XX) 3 Statistics (62-XX) 3 Computer science (68-XX) 3 Quantum theory (81-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Information and communication theory, circuits (94-XX) 2 History and biography (01-XX) 2 Algebraic geometry (14-XX) 2 Topological groups, Lie groups (22-XX) 2 Functions of a complex variable (30-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Differential geometry (53-XX) 2 Fluid mechanics (76-XX) 2 Optics, electromagnetic theory (78-XX) 2 Biology and other natural sciences (92-XX) 1 General and overarching topics; collections (00-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Associative rings and algebras (16-XX) 1 Special functions (33-XX) 1 Sequences, series, summability (40-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral equations (45-XX) 1 Convex and discrete geometry (52-XX) 1 Algebraic topology (55-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX)