Java Number Cruncher: The Java Programmers Guide to Numerical Computing

Atkinson, L.V., and P.J. Harley, An Introduction to Numerical Methods with Pascal , London: Addison-Wesley, 1983.

Chapra, Seven C., and Raymond P. Canale, Numerical Methods for Engineers , 3rd edition, New York: WCB/McGraw-Hill, 1998.

Polynomial regression is discussed by Chapra and Canale in Section 17.2.

Cheny, Ward, and David Kincaid, Numerical Mathematics and Computing , 4th edition, Pacific Grove, CA: Brooks/Cole, 1999.

Forsythe, George, Michael A. Malcolm, and Cleve B. Moler, Computer Methods for Mathematical Computations , Englewood Cliffs, NJ: Prentice-Hall, 1977.

Forsythe is the classic reference for solving systems of linear equations using LU decomposition. It contains a constructive proof that matrix A can be factored into matrices L and U, as well as error analyses of the algorithms. It has program listings in Algol, FORTRAN, and PL/I. For more contemporary textbooks that describe Gaussian elimination and LU decomposition, see Chapra and Canale, Sections 9.1 C9.4 and 10.1; Cheney and Kincaid, Sections 6.1 and 6.2; Woodford and Phillips, in Chapter 1; Atkinson and Harley, Chapter 4; and Scheid, Chapter 26.

Monahan, John F., Numerical Methods of Statistics , Cambridge, UK: Cambridge University Press, 2001. Monahan provides advanced coverage of polynomial regression in Chapter 5.

Scheid, Francis, Numerical Analysis , New York: McGraw-Hill, 1988.

Woodford, C., and C. Phillips, Numerical Methods with Worked Examples , London: Chapman and Hall, 1997. Woodford and Phillips discuss polynomial regression in Section 3.4.2.