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Ralph Byers 1955–2007. (English) Zbl 1140.65301

MSC:

65-03 History of numerical analysis
93-03 History of systems and control theory
01A60 History of mathematics in the 20th century

Biographic References:

Byers, Ralph
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References:

[1] R. Byers, Hamiltonian and Symplectic Algorithms for the Algebraic Riccati Equation, Ph.D. Thesis, Cornell University, Department Computer Science, Ithaca, NY, 1983.; R. Byers, Hamiltonian and Symplectic Algorithms for the Algebraic Riccati Equation, Ph.D. Thesis, Cornell University, Department Computer Science, Ithaca, NY, 1983.
[2] Byers, R., A LINPACK style condition estimator for the equation \(AX - XB^T = C\), IEEE Trans. Automat. Control, AC-29, 10, 926-927 (1984) · Zbl 0544.65027
[3] Byers, R.; Mehrmann, V., Symmetric updating of the solution of the algebraic Riccati equation, (Methods of Operations Research, (Proceedings of the 10th Symposium on Operations Research), Universität München, August 26-28, 1985 (1985), Verlag Anton Hain), 117-125 · Zbl 0664.93024
[4] Byers, R., Numerical condition of the algebraic Riccati equation, Contemp. Math., 47, 35-49 (1985)
[5] Byers, R., Numerical stability and instability in matrix sign function based algorithms, (Byrnes, C. I.; Linquist, A., Computational and Combinatorial Methods in Systems Theory (1986), North-Holland: North-Holland New York), 185-200
[6] R. Byers, A Hamiltonian QR algorithm, SIAM J. Sci. Statist. Comput. 7 (1986) 212-229, Reprinted in Numerical Linear Algebra Techniques for System and Control, in: Rajni V. Patel, Alan J. Laub, Paul Van Dooren, (Eds.), IEEE Press, New York, 1994, pp. 469-494.; R. Byers, A Hamiltonian QR algorithm, SIAM J. Sci. Statist. Comput. 7 (1986) 212-229, Reprinted in Numerical Linear Algebra Techniques for System and Control, in: Rajni V. Patel, Alan J. Laub, Paul Van Dooren, (Eds.), IEEE Press, New York, 1994, pp. 469-494.
[7] Byers, R.; Harris, B.; Kwong, M., Weighted means and oscillation conditions for second order matrix differential equations, J. Differential Equations, 61, 2, 164-177 (1986) · Zbl 0609.34042
[8] Byers, R.; Nash, S., On the singular “vectors” of the Lyapunov operator, SIAM J. Algebraic Discrete Methods, 8, 1, 59-66 (1987) · Zbl 0633.65042
[9] Byers, R., Solving the algebraic Riccati equation with the matrix sign function, Linear Algebra Appl., 85, 267-279 (1987) · Zbl 0611.65027
[10] R. Byers, A bisection method for measuring the distance of a stable matrix to the unstable matrices, SIAM J. Sci. Statist. Comput. 9 (1988) 875-881, Reprinted in Numerical Linear Algebra Techniques for System and Control, in: Rajni V. Patel, Alan J. Laub, Paul Van Dooren, (Eds.), IEEE Press, New York, 1994, pp. 219-224.; R. Byers, A bisection method for measuring the distance of a stable matrix to the unstable matrices, SIAM J. Sci. Statist. Comput. 9 (1988) 875-881, Reprinted in Numerical Linear Algebra Techniques for System and Control, in: Rajni V. Patel, Alan J. Laub, Paul Van Dooren, (Eds.), IEEE Press, New York, 1994, pp. 219-224. · Zbl 0658.65044
[11] Byers, R.; Nash, S., Approaches to robust pole assignment, Internat. J. Control, 49, 97-117 (1989) · Zbl 0666.93042
[12] Bunse-Gerstner, A.; Byers, R.; Mehrmann, V., A quaternion QR algorithm, Numer. Math., 55, 83-95 (1989) · Zbl 0681.65024
[13] A. Bunse-Gerstner, R. Byers, V. Mehrmann, Numerical methods for algebraic Riccati equations, in: Proceedings of the Workshop on the Riccati Equation in Control, Systems and Signals, Como, Italy, June 1989, pp. 107-116.; A. Bunse-Gerstner, R. Byers, V. Mehrmann, Numerical methods for algebraic Riccati equations, in: Proceedings of the Workshop on the Riccati Equation in Control, Systems and Signals, Como, Italy, June 1989, pp. 107-116.
[14] R. Byers, Detecting nearly uncontrollable pairs, in: M.A. Kaashoek, J.H. van Schuppen, A.C.M. Ran, (Ed.), Signal Processing, Scattering and Operator Theory, and Numerical Methods, Proceedings of the International Symposium MTNS-89, Amsterdam, vol. III, Birkhäuser, Boston, 1990, pp. 447-457.; R. Byers, Detecting nearly uncontrollable pairs, in: M.A. Kaashoek, J.H. van Schuppen, A.C.M. Ran, (Ed.), Signal Processing, Scattering and Operator Theory, and Numerical Methods, Proceedings of the International Symposium MTNS-89, Amsterdam, vol. III, Birkhäuser, Boston, 1990, pp. 447-457. · Zbl 0722.93010
[15] Byers, R., A Hamiltonian-Jacobi algorithm, IEEE Trans. Automat. Control, AC-35, 5, 566-570 (1990) · Zbl 0706.65066
[16] Bunse-Gerstner, A.; Byers, R.; Mehrmann, V.; Nichols, N. K., Numerical computation of an analytic singular value decomposition of a matrix valued function, Numer. Math., 60, 1-39 (1991) · Zbl 0743.65035
[17] A. Bunse-Gerstner, R. Byers, V. Mehrmann, A chart of numerical methods for structured eigenvalue problems, SIAM J. Matrix Anal. Appl. 13 (1992) 419-453, Reprinted in Numerical Linear Algebra Techniques for System and Control, Rajni V. Petel, Alan J. Laub, Paul Van Dooren, (Ed.), IEEE Press, New York, 1994, pp. 437-468.; A. Bunse-Gerstner, R. Byers, V. Mehrmann, A chart of numerical methods for structured eigenvalue problems, SIAM J. Matrix Anal. Appl. 13 (1992) 419-453, Reprinted in Numerical Linear Algebra Techniques for System and Control, Rajni V. Petel, Alan J. Laub, Paul Van Dooren, (Ed.), IEEE Press, New York, 1994, pp. 437-468. · Zbl 0757.65040
[18] Bunse-Gerstner, A.; Byers, R.; Mehrmann, V., Numerical methods for simultaneous diagonalization, SIAM J. Matrix Anal. Appl., 14, 4, 927-949 (1993) · Zbl 0786.65030
[19] Byers, R.; Nichols, N. K., On the stability radius of a generalized state-space system, Linear Algebra Appl., 188/189, 113-134 (1993) · Zbl 0783.65056
[20] P. Benner, R. Byers, Step size control for Newton’s method applied to algebraic Riccati equations, in: John Lewis (Ed.), Proceedings of the Fifth SIAM Conference on Applied Linear Algebra, 1994, pp. 177-181.; P. Benner, R. Byers, Step size control for Newton’s method applied to algebraic Riccati equations, in: John Lewis (Ed.), Proceedings of the Fifth SIAM Conference on Applied Linear Algebra, 1994, pp. 177-181. · Zbl 0819.65078
[21] Byers, R., The descriptor controllability radius, (Helmke, Uwe; Mennicken, Reinhard; Saurer, Josef, Systems and Networks: Mathematical Theory and Applications, Proceedings of the International Symposium, MTNS ’93 held in Regensburg, Germany, August 2-6, 1993, vol. II (1994), Akademie Verlag GmbH: Akademie Verlag GmbH Berlin), 85-88 · Zbl 0925.93084
[22] R. Byers, N. Rhee, Cyclic Schur and Hessenberg-Schur numerical methods for solving periodic Lyapunov and Sylvester equations, unpublished.; R. Byers, N. Rhee, Cyclic Schur and Hessenberg-Schur numerical methods for solving periodic Lyapunov and Sylvester equations, unpublished.
[23] R. Byers, C. He, V. Mehrmann, On the matrix sign function method for the computation of invariant subspaces, in: Proceedings of the 1996 IEEE International Symposium on Conputer-Aided Control System Design, Dearborn, Michigan, USA, September 15-18, 1996, 1996, pp. 71-76.; R. Byers, C. He, V. Mehrmann, On the matrix sign function method for the computation of invariant subspaces, in: Proceedings of the 1996 IEEE International Symposium on Conputer-Aided Control System Design, Dearborn, Michigan, USA, September 15-18, 1996, 1996, pp. 71-76.
[24] P. Benner, R. Byers, Disk functions and their relationship to the matrix sign function, in: Proceedings of the 4th European Control Conference, Brussels, July 1-4, 1997.; P. Benner, R. Byers, Disk functions and their relationship to the matrix sign function, in: Proceedings of the 4th European Control Conference, Brussels, July 1-4, 1997.
[25] Byers, R.; He, C.; Mehrmann, V., The matrix sign function method and the computation of invariant subspaces, SIAM J. Matrix Anal. Appl., 18, 615-632 (1997) · Zbl 0874.65031
[26] Byers, R.; Geerts, T.; Mehrmann, V., Descriptor systems without controllability at infinity, SIAM J. Control Optim., 35, 462-479 (1997) · Zbl 0871.93021
[27] Byers, R.; Kunkel, P.; Mehrmann, V., Regularization of linear descriptor systems with variable coefficients, SIAM J. Control Optim., 35, 117-133 (1997) · Zbl 0895.93026
[28] P. Benner, R. Byers, An arithmetic for matrix pencils, in: A. Beghi, L. Finesso, G. Picci (Eds.), Mathematical Theory of Networks and Systems, Proceedings of the MTNS-98 symposium held in Padova, Italy, July 1998, Il Poligrafo s.r.l., via Turazza, 19, 35128 Padova, Italy, 1998, pp. 573-576.; P. Benner, R. Byers, An arithmetic for matrix pencils, in: A. Beghi, L. Finesso, G. Picci (Eds.), Mathematical Theory of Networks and Systems, Proceedings of the MTNS-98 symposium held in Padova, Italy, July 1998, Il Poligrafo s.r.l., via Turazza, 19, 35128 Padova, Italy, 1998, pp. 573-576. · Zbl 1101.65046
[29] Byers, R.; He, C.; Mehrmann, V., Where is the nearest non-regular pencil?, Linear Algebra Appl., 285, 81-105 (1998) · Zbl 0935.15013
[30] Benner, P.; Byers, R., An exact line search method for solving generalized continuous-time algebraic Riccati equations, IEEE Trans. Automat. Control, AC-43, 101-107 (1998) · Zbl 0908.93026
[31] R. Byers, E. Barth, P. Benner,; R. Byers, E. Barth, P. Benner,
[32] P. Benner, R. Byers, V. Mehrmann, H. Xu, Numerical solution of linear quadratic control problems for descriptor systems, in: Oscar Gonzalez, (Ed.), Proceedings of the 1999 IEEE International Symposium on Computer Aided Control System Design, Kohala Coast - Island of Hawai’i, Hawai’i, August 22-27, 1999, CDROM Omnipress, 2600 Anderson Street Madison, Wisconsin 53704, 1999, pp. 46-51.; P. Benner, R. Byers, V. Mehrmann, H. Xu, Numerical solution of linear quadratic control problems for descriptor systems, in: Oscar Gonzalez, (Ed.), Proceedings of the 1999 IEEE International Symposium on Computer Aided Control System Design, Kohala Coast - Island of Hawai’i, Hawai’i, August 22-27, 1999, CDROM Omnipress, 2600 Anderson Street Madison, Wisconsin 53704, 1999, pp. 46-51.
[33] P. Benner, R. Byers, An arithmetic for rectangular matrix pencils, in: Oscar Gonzalez, (Ed.), Proceedings of the 1999 IEEE International Symposium on Computer Aided Control System Design, Kohala Coast - Island of Hawai’i, Hawai’i, August 22-27, 1999, CDROM Omnipress, 2600 Anderson Street Madison, Wisconsin 53704, 1999, pp. 75-80.; P. Benner, R. Byers, An arithmetic for rectangular matrix pencils, in: Oscar Gonzalez, (Ed.), Proceedings of the 1999 IEEE International Symposium on Computer Aided Control System Design, Kohala Coast - Island of Hawai’i, Hawai’i, August 22-27, 1999, CDROM Omnipress, 2600 Anderson Street Madison, Wisconsin 53704, 1999, pp. 75-80.
[34] Bunse-Gerstner, A.; Byers, R.; Mehrmann, V.; Nichols, N. K., Feedback design for regularizing descriptor systems, Linear Algebra Appl., 299, 119-151 (1999) · Zbl 0944.65082
[35] P. Benner, R. Byers, V. Mehrmann, H. Xu. Numerical methods for linear quadratic and \(H_{\operatorname{\infty;}} \); P. Benner, R. Byers, V. Mehrmann, H. Xu. Numerical methods for linear quadratic and \(H_{\operatorname{\infty;}} \) · Zbl 0928.93017
[36] R. Byers, E. Barth.; R. Byers, E. Barth.
[37] Benner, P.; Byers, R.; Faßbender, H.; Mehrmann, V.; Watkins, D., Cholesky-like factorizations of skew-symmetric matrices, Elect. Trans. Numer. Anal., 11, 85-93 (2000) · Zbl 0963.65033
[38] Benner, P.; Byers, R.; Barth, E., Algorithm 800: Fortran 77 subroutines for computing the eigenvalues of Hamiltonian matrices I: The square reduced method, ACM Trans. Math. Software, 26, 49-77 (2000) · Zbl 1137.65338
[39] Benner, P.; Byers, R.; Quintana-Ortí, E. S.; Quintana-Ortí, G., Solving algebraic Riccati equations on parallel computers using Newton’s method with exact line search, Parallel Computing, 26, 10, 1345-1368 (2000) · Zbl 0949.65041
[40] Benner, P.; Byers, R., Evaluating products of matrix pencils and collapsing matrix products for parallel computation, Numer. Linear Algebra Appl., 8, 357-380 (2001) · Zbl 1055.65053
[41] Benner, P.; Byers, R.; Mayo, R.; Quintana-Qrtí, E. S.; Hernandez, V., Parallel algorithms for LQ optimal control of discrete-time periodic linear systems, J. Parallel Distributed Comput., 62, 306-325 (2002) · Zbl 1008.93035
[42] Benner, P.; Byers, R.; Mehrmann, V.; Xu, H., Numerical computation of deflating subspaces of skew-Hamiltonian/Hamiltonian pencils, SIAM J. Matrix Anal. Appl., 24, 1, 165-190 (2002) · Zbl 1035.49022
[43] Braman, K.; Byers, R.; Mathias, R., The multi-shift QR algorithm. Part I: maintaining well focused shifts and level 3 performance, SIAM J. Matrix Anal. Appl., 23, 929-947 (2002) · Zbl 1017.65031
[44] Braman, K.; Byers, R.; Mathias, R., The multi-shift QR algorithm. Part II: aggressive early deflation, SIAM J. Matrix Anal. Appl., 23, 948-973 (2002) · Zbl 1017.65032
[45] P. Benner, R. Byers, A structure-preserving method for generalized algebraic Riccati equations based on pencil arithmetic, in: Proceedings of the European Control Conference ECC’03, September 1-4, 2003, Cambridge, UK (CD Rom), 2003.; P. Benner, R. Byers, A structure-preserving method for generalized algebraic Riccati equations based on pencil arithmetic, in: Proceedings of the European Control Conference ECC’03, September 1-4, 2003, Cambridge, UK (CD Rom), 2003.
[46] P. Benner, R. Byers, V. Mehrmann, H. Xu, A robust numerical method for optimal \(H_{\operatorname{\infty;}} \); P. Benner, R. Byers, V. Mehrmann, H. Xu, A robust numerical method for optimal \(H_{\operatorname{\infty;}} \) · Zbl 1124.93022
[47] Byers, R.; Kressner, D., On the condition of a complex eigenvalue under real perturbations, BIT, 44, 2, 209-214 (2004) · Zbl 1071.15004
[48] K. Braman, R. Byers,; K. Braman, R. Byers,
[49] Byers, R.; Kressner, D., Structured condition numbers for invariant subspaces, SIAM J. Matrix Anal. Appl., 28, 326-347 (2006) · Zbl 1116.65052
[50] Benner, P.; Byers, R., An arithmetic for matrix pencils: theory and new algorithms, Numer. Math., 103, 539-573 (2006) · Zbl 1101.65046
[51] Byers, R.; Datta, B. N., Vector and matrix norms, error analysis, efficiency and stability, (Hogben, Leslie; Brualdi, Richard; Greenbaum, Anne; Mathias, Roy, Handbook of Linear Algebra. Handbook of Linear Algebra, Discrete Mathematics and Applications, vol. 39 (2006), CRC Press), (Chapter 37)
[52] R. Byers, LAPACK 3.1; R. Byers, LAPACK 3.1
[53] Benner, P.; Byers, R.; Mehrmann, V.; Xu, H., A robust numerical method for the \(\gamma \)-iteration in \(H_\infty\) control, Linear Algebra Appl., 425, 548-570 (2007) · Zbl 1124.93022
[54] Byers, R.; Mehrmann, V.; Xu, H., A structured staircase algorithm for skew-symmetric/symmetric pencils, Elect. Trans. Numer. Anal., 26, 1-13 (2007) · Zbl 1113.65065
[55] R. Byers, H. Xu, A new scaling for Newton’s iteration for the polar decomposition and its backward stability, SIAM J. Matrix Anal. Appl., submitted for publication.; R. Byers, H. Xu, A new scaling for Newton’s iteration for the polar decomposition and its backward stability, SIAM J. Matrix Anal. Appl., submitted for publication. · Zbl 1170.65019
[56] R. Byers, V. Mehrmann, H. Xu, Staircase forms and trimmed linearizations for structured matrix polynomials, Linear Algebra Appl., in press, doi:10.1016/j.laa.2008.01.005; R. Byers, V. Mehrmann, H. Xu, Staircase forms and trimmed linearizations for structured matrix polynomials, Linear Algebra Appl., in press, doi:10.1016/j.laa.2008.01.005 · Zbl 1155.65026
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