Abstract
The singular value decomposition (SVD), closely related to matrix eigenvalue-eigenvector decompositions, is a powerful tool for analyzing linear systems. Like all mathematical tools it has its legitimate uses, but it can also be abused, of which we will have more to say in Section 8.4.
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References
Acton, F.S. (1970). Numerical Methods that (Usually) Work ( Harper and Row, New York).
Andrews, H.C. and Hunt, B.R. (1977). Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J.).
Branham, R.L., Jr. (1979). Least Squares Solution of Ill-Conditioned Systems, Astron. J., 84, p. 1632.
Branham, R.L., Jr. (1980). Least Squares Solution of Ill-Conditioned Systems, II, Astron. J., 85, p. 1520.
Branham, R.L., Jr. (1989). A Program for Total (Orthogonal) Least Squares in Compact Storage Mode, Computers in Physics, 3, p. 42.
Fike, C.T. (1968). Computer Evaluation of Mathematical Functions (Prentice-Hall, Englewood Cliffs, N.J.).
Forsythe, G., Malcolm, M.A., and Moler, C.B. (1977). Computer Methods for Mathematical Computations (Prentice-Hall, Englewood Cliffs, N.J.).
Forsythe, G. and Moler, C.B. (1967). Computer Solution of Linear Algebraic Systems (Prentice-Hall, Englewood Cliffs, N.J.).
Golub, G.H. and Reinsch, C. (1970). Singular Value Decomposition and Least Squares Solutions, Numer. Math., 14, p. 403.
Golub, G.H. and Van Loan, C.F. (1980). An Analysis of the Total Least Squares Problem, SIAM J. Numer. Anal, 17, p. 883.
Lawson, C.L. and Hanson, R.J. (1974). Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, N.J.).
Mathews, J. and Walker, R.L. (1964). Mathematical Methods of Physics (W.A. Benjamin, New York). A second edition of this work was published in 1970. The author has the first edition, referenced in the text.
Pratt, W.K. (1978). Digital Image Processing ( Wiley, New York).
Press, W.H., Flannery, B.P., Teukolsky, S.A., and Vetterling, W.T. (1986). Numerical Recipes: The Art of Scientific Computing ( Cambridge University Press, Cambridge).
Späth, H. and Watson, G.A. (1987). On Orthogonal Linear L 1 Approximation, Numer. Math., 51, p. 531.
Vandergraft, J.S. (1983). Introduction to Numerical Computations, 2nd ed. ( Academic Press, New York).
Wilkinson, J.H. (1965). The Algebraic Eigenvalue Problem ( Oxford University Press, Oxford).
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© 1990 Springer-Verlag New York Inc.
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Branham, R.L. (1990). The Singular Value Decomposition. In: Scientific Data Analysis. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3362-6_8
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DOI: https://doi.org/10.1007/978-1-4612-3362-6_8
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