Reference
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Bibliography
Most of the matrix decomposition algorithms implemented by this library follow the descriptions
and reference C++ implementations given in Chapter 2, "Solution of Linear Algebraic Equations", of
Numerical Recipes: The Art of Scientific Computing, 3rd Edition (Cambridge University Press,
2007). RQDecomposer and the norm estimation classes are instead based on the external references
listed below. The table maps each class to the section or page it is based on.
| Class | Reference | Section / pages |
|---|---|---|
Numerical Recipes, 3rd Edition |
2.1 "Gauss-Jordan Elimination", pp. 41-46 |
|
Numerical Recipes, 3rd Edition |
2.3 "LU Decomposition and Its Applications", pp. 48-56 |
|
Numerical Recipes, 3rd Edition |
2.6 "Singular Value Decomposition", pp. 65-75 |
|
Numerical Recipes, 3rd Edition |
2.9 "Cholesky Decomposition", pp. 100-102 |
|
Numerical Recipes, 3rd Edition |
2.10 "QR Decomposition", pp. 102-106 |
|
Wikipedia, "QR decomposition" |
||
Mathematics Stack Exchange, "RQ decomposition" |
https://math.stackexchange.com/questions/1640695/rq-decomposition |
|
Wikipedia, "Matrix norm" |
||
Wikipedia, "Norm (mathematics)" |
Cited references
Numerical Recipes' own chapter 2 points to these works for a deeper treatment of linear algebra, and they are also cited directly in this library’s class-level Javadoc:
-
Golub, G.H., and Van Loan, C.F. 1996, Matrix Computations, 3rd ed. (Baltimore: Johns Hopkins University Press).
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Wilkinson, J.H., and Reinsch, C. 1971, Linear Algebra, vol. II of Handbook for Automatic Computation (New York: Springer).
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Wilkinson, J.H. 1965, The Algebraic Eigenvalue Problem (New York: Oxford University Press).
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Forsythe, G.E., and Moler, C.B. 1967, Computer Solution of Linear Algebraic Systems (Englewood Cliffs, NJ: Prentice-Hall).
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Forsythe, G.E., Malcolm, M.A., and Moler, C.B. 1977, Computer Methods for Mathematical Computations (Englewood Cliffs, NJ: Prentice-Hall).
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Anderson, E., et al. 1999, LAPACK User’s Guide, 3rd ed. (Philadelphia: S.I.A.M.). Online with software at www.netlib.org/lapack.
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Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P. 2007, Numerical Recipes: The Art of Scientific Computing, 3rd ed. (Cambridge, UK: Cambridge University Press), Chapter 2, "Solution of Linear Algebraic Equations", pp. 37-109. Available at: numerical.recipes.
-
Wikipedia contributors, "QR decomposition", Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/QR_decomposition.
-
Wikipedia contributors, "Matrix norm", Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Matrix_norm.
-
Wikipedia contributors, "Norm (mathematics)", Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Norm_(mathematics).
-
Mathematics Stack Exchange contributors, "RQ decomposition", https://math.stackexchange.com/questions/1640695/rq-decomposition.