Publications of Greg Ammar

• An Efficient QR Algorithm for a Hessenberg Submatrix of a Unitary Matrix (with W.B. Gragg and C. He), in New Directions and Applications in Control Theory, W.P. Dayawansa, A. Lindquist and Y. Zhou, eds., Lecture Notes in Control and Information Sciences, Vol. 321, Springer-Verlag, 2005, pp. 1-14.
  
  
• Polynomial Zerofinders Based on Szegő Polynomials (with D. Calvetti, W.B. Gragg and L. Reichel), J. Comput. Appl. Math., 127 (2001), 1-16. PDF format.   |   Postscript format.
  
  
• Computation of Gauss-Kronrod Quadrature Rules with Non-Positive Weights (with D. Calvetti and L. Reichel), Electronic Trans. Numerical Anal., 9 (1999), 26-38. PDF format.   |   Postscript format.
  
  
• Schur-Like Forms for Matrix Lie Groups, Lie Algebras and Jordan Algebras, (with C. Mehl and V. Mehrmann), Linear Algebra and Its Applications, 287 (1999), 11-39. PDF format.   |   Postscript format.
  
  
• Classical Foundations of Algorithms for Solving Positive Definite Toeplitz Equations, Calcolo, 33 (1996), 99-113. An HTML version is also available. PDF format.   |   Postscript format.
  
  
• Continuation Methods for the Computation of Zeros of Szegő Polynomials (with D. Calvetti and L. Reichel), Linear Algebra and Its Applications, 249 (1996), 125-155. PDF format   |   Postscript format.
  
  
• On an Inverse Eigenvalue Problem for Unitary Hessenberg Matrices (with C. He), Linear Algebra and Its Applications, 218 (1995), pp. 263--271. PDF format   |   Postscript format.
  
  
• Algorithm 730: An Implementation of a Divide and Conquer Algorithm for the Unitary Eigenproblem (with L. Reichel and D. C. Sorensen), ACM Trans. Math. Softw., Vol. 20, 1994, p. 161. (Mathematical software.)
  
  
• Schur Flows for Orthogonal Hessenberg Matrices (with W.B. Gragg), in Hamiltonian and Gradient Flows, Algorithms and Control, A. Bloch, ed., Fields Institute Communications, Vol. 3, American Mathematical Society, Providence, 1994, pp. 27-24. PDF format   |   Postscript format.
  
  
• Computing the Poles of Autoregressive Models from the Reflection Coefficients (with D. Calvetti and L. Reichel), Proceedings of the Thirty-First Annual Allerton Conference on Communication, Control, and Computing, Monticello, IL, October, 1993, pp. 255-264. PDF format   |   Postscript format.
  
  
• A Multishift Algorithm for the Numerical Solution of Algebraic Riccati Equations (with P. Benner and V. Mehrmann), Electronic Transactions on Numerical Analysis, Vol. 1 (1993), pp. 33-48. PDF format   |   Postscript format.
  
  
• Direct and Inverse Unitary Eigenproblems in Signal Processing: An Overview (with W.B. Gragg and L. Reichel), in Linear Algebra for Large Scale and Real-Time Applications, M.S. Moonen, G.H. Golub and B.L.R. De Moor, eds., Kluwer Academic Publishers, Dordrecht/Boston, 1993, pp. 341-343. PDF format   |   Postscript format. An HTML version of this paper is also available.
  
  
• An Analogue for Szegő Polynomials of the Clenshaw Algorithm (with W.B. Gragg and L. Reichel), J. Computational Appl. Math., 46 (1993) pp., 211-216. PDF format   |   Postscript format.
  
  
• Inverse problems for orthogonal matrices, Toda flows and signal processing (with L. Faybusovich and W.B. Gragg), in Proceedings of 31st IEEE Conference on Decision and Control, Dec. 16-18, Tucson, Arizona, IEEE, 1992, pp. 1488-1493.
  
  
• Downdating Szegő Polynomials and Data Fitting Applications (with W.B. Gragg and L. Reichel), Linear Algebra and Its Applications, 172 (1992), pp. 315-336. An HTML version of this paper is available.
  
  
• An Implementation of a Divide and Conquer Algorithm for the Unitary Eigenproblem (with L. Reichel and D. C. Sorensen), ACM Trans. Math. Software, 18 (1992), pp 292-307.
  
  
• A Geometric Perspective on Condensed Forms for Hamiltonian Matrices (with V. Mehrmann), in Computation and Control II, K.L. Bowers and J. Lund, eds., Birkhäuser, Boston, 1991, 1-11.
  
  
• The Geometry of the Matrix Riccati Equation and Associated Eigenvalue Methods (with C. F. Martin), in The Riccati Equation, S. Bittanti, A. Laub, and J. Willems, eds., Springer-Verlag, Berlin, 1991, 113-126.
  
  
• Discrete Least Squares Approximation by Trigonometric Polynomials (with W. B. Gragg and L. Reichel), Mathematics of Computation, 57, 1991, 273-289.
  
  
• On Hamiltonian and Symplectic Hessenberg Forms (with V. Mehrmann), Linear Algebra and Its Applications, 149, 1991, 55-72.
  
  
• Exponential Interpolation: Theory and Numerical Algorithms (with W. Dayawansa and C.F. Martin), Applied Mathematics and Computation, 41, 1991, 189-232.
  
  
• A Variant of the Gohberg-Semencul Formula Involving Circulant Matrices (with P. Gader), SIAM J. Matrix Anal. Appl., 12, 1991, 534-540.
  
  
• O(n²) Reduction Algorithms for the Construction of a Band Matrix from Spectral Data (with W.B. Gragg), SIAM J. Matrix Anal. Appl., 12, 1991, 426-431.
  
  
• A Divide and Conquer Method for the Unitary Eigenproblem and Applications (Abstract) (with W.B. Gragg and L. Reichel), in Numerical Linear Algebra, Digital Signal Processing, and Parallel Algorithms, G.H. Golub and P. Van Dooren, eds., Springer-Verlag, Berlin, 1991, 579-580.
  
  
• Constructing a Unitary Hessenberg Matrix from Spectral Data (with W.B. Gragg and L. Reichel), in Numerical Linear Algebra, Digital Signal Processing, and Parallel Algorithms, G.H. Golub and P. Van Dooren, eds., Springer-Verlag, Berlin, 1991, 385-396. PDF format   |   Postscript format.
  
  
• System Identification and Exponential Interpolation (with W. Dayawansa and C. Martin), Texas Tech Mathematics Series, Vol. 16, Lubbock, TX, 1990, 1-28.
  
  
• Identification of Linear Systems by Prony's Method (with D. Cheng, W. Dayawansa and C. Martin), in Robust Control of Linear Systems and Nonlinear Control: Proceedings of the International Symposium MTNS-89, Volume II, M.A. Kaashoek, J.H. van Schuppen and A.C.N. Ran, eds., Birkhäuser, Boston, 1990, 483-488.
  
  
• New Decompositions of the Inverse of a Toeplitz Matrix (with P. Gader), in Signal Processing, Scattering and Operator Theory, and Numerical Methods: Proceedings of the International Symposium MTNS-89, Volume III, M.A. Kaashoek, J.H. van Schuppen and A.C.N. Ran, eds., Birkhäuser, Boston, 1990, 421-428.
  
  
• Fast Approximation of Dominant Harmonics by Solving an Orthogonal Eigenvalue Problem (with L. Reichel), Proc. Second IMA Conference on Mathematics in Signal Processing, J. McWhirter et al., eds., Oxford University Press, 1990.
  
  
• Numerical Experience with a Superfast Real Toeplitz Solver (with W. B. Gragg), Linear Algebra and its Applications, 121, 1989, 185-206.
  
  
• Superfast Solution of Real Positive Definite Toeplitz Systems (with W. B. Gragg), SIAM J. Matrix Anal. Appl., 9, 1988, pp. 61-76. This paper also appears in Linear Algebra in Signals, Systems, and Control, B.N. Datta et al., eds., SIAM, Philadelphia, 1988, pp. 107-125. PDF format   |   Postscript format.
  
  
• Determination of Pisarenko Frequency Estimates as Eigenvalues of an Orthogonal Matrix (with W. B. Gragg and L. Reichel), in Advanced Algorithms and Architectures for Signal Processing II (F.T. Luk, ed.), Proc. SPIE 826, 1987, pp. 143-145.
  
  
• Geometric Aspects of Hessenberg Matrices, Contemporary Mathematics 68, American Mathematical Society, Providence, RI, 1987, pp. 1-21.
  
  
• The Generalized Schur Algorithm for the Superfast Solution of Toeplitz Systems (with W.B. Gragg), in Rational Approximation and its Applications in Mathematics and Physics, J. Gilewicz, M. Pindor and W. Siemaszko, eds., Lecture Notes in Mathematics 1237, Springer-Verlag, Berlin, 1987, pp. 315-330. PDF format   |   Postscript format.
  
  
• On the Eigenproblem for Orthogonal Matrices (with W. B. Gragg and L. Reichel), Proceedings of the 25th Conference on Decision and Control (Athens, Greece, December 1986), Institute of Electrical and Electronics Engineers, New York, 1986, pp. 1963-1966.
  
  
• Implementation and Use of the Generalized Schur Algorithm (with W.B. Gragg), in Computational and Combinatorial Methods in Systems Theory, C.I. Byrnes and A. Lindquist, eds., North-Holland, Amsterdam, 1986, pp. 265-280.
  
  
• Inverse Eigenvalue Methods and Flag Manifolds, in Computational and Combinatorial Methods in Systems Theory, C.I. Byrnes and A. Lindquist, eds., North-Holland, Amsterdam, 1986, pp. 177-184.
  
  
• The Geometry of Matrix Eigenvalue Methods (with Clyde Martin), Acta Applicandae Mathematicae, 5, 1986, pp. 239-278.
  
  
• Grassmannians, Riccati Equations, and Numerical Linear Algebra, Proceedings of the 24th IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers, New York, 1985, pp. 1784-1787.
  
  
• Riccati Equations and the Matrix Eigenvalue Methods, Proceedings of the Berkeley-Ames Conference on Nonlinear Problems in Control and Fluid Dynamics, L.R. Hunt and C.F. Martin, eds., Math Sci Press, Brookline, MA, 1984, pp. 63-79.
  
  
• Riccati Equations and the Matrix Eigenvalue Problem (with Clyde Martin), Proceedings of the Twentieth Annual Allerton Conference on Communication, Computing and Control, Monticello, Illinois, 1982.

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