Abstract
This chapter presents an overview of the most important algorithms for solving symmetric linear systems as appearing in the nonrecursive covariance case of linear prediction and several other useful techniques for matrix computations which will be required throughout this book. The techniques presented here have also a wide range of applications in the field of numerical analysis [3.1–4].
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References
Chapter 3
C.L. Lawson, R.J. Hanson: Solving Least-Squares Problems (Prentice Hall, Englewood Cliffs, NJ 1974)
H.R. Schwarz, H. Rutishauser, E. Stiefel: Numerical Analysis of Symmetric Matrices (Prentice-Hall, Englewood Cliffs, NJ 1973)
F.S. Acton: Numerical Methods that Work (Harper and Row, New York 1970)
G.H. Golub: Numerical methods for solving linear least-squares problems. Numer. Math. 7, 206–216 (1965)
B.W. Dickinson: Estimation of partial correlation matrices using Cholesky decomposition. IEEE Trans. Autom. Control 24, 302–305 (1979)
B.W. Dickinson, J.M. Turner: Reflection coefficient estimation using Cholesky decomposition. IEEE Trans. ASSP 27, 146–149 (1979)
D. Gibson: On reflection coefficients and the Cholesky decomposition. IEEE Trans. ASSP 25, 93–96 (1977)
J.W. Givens: Numerical computation of the characteristic values of a real symmetric matrix. Oak Ridge National Laboratory, ORNR 1574, Internal Report (1954)
W.M. Gentleman: Least-squares computation by Givens transformations without square roots. J. Inst. Math. Appl. 12, 329–336 (1973)
S. Hammarling: A note on modifications to the Givens plane rotation. J. Inst. Math. Appl. 13, 215–218 (1974)
J.G. Nash, S. Hansen: Modified Faddeeva algorithm for concurrent execution of linear algebraic operations. IEEE Trans. Comput. 37, 129–137 (1988)
J. Götze, U. Schwiegelshohn: An orthogonal method for solving systems of linear equations without square roots and with few divisions. Proc. Int. Conf. on ASSP, Glasgow (1989) pp. 1298–1300
A.S. Householder: The Theory of Matrices in Numerical Analysis (Blaisdell, New York 1964)
A.O. Steinhardt: Householder transforms in signal processing. IEEE ASSP Magazine 5, 4–12 (1988)
C. Rader, A. Steinhardt: Hyperbolic Householder transformations. IEEE Trans. ASSP 34, 1589–1602 (1986)
E.F. Deprettere (ed.): Singular Value Decomposition and Signal Processing: Algorithms, Applications, and Architectures (North-Holland, Amsterdam 1989)
R. Penrose: A general inverse for matrices. Proc. Cambridge Philos. Soc. 51, 406–413 (1955)
G.H. Golub, C. Reinsch: “Singular Value Decomposition and Least-Squares Solutions”, in Handbook for Automatic Computation II, Linear Algebra, ed. by J.H. Wilkinson, C. Reinsch (Springer, New York 1971)
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Strobach, P. (1990). Classical Algorithms for Symmetric Linear Systems. In: Linear Prediction Theory. Springer Series in Information Sciences, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75206-3_3
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DOI: https://doi.org/10.1007/978-3-642-75206-3_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-75208-7
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