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.

Conte, Samuel D., and Carl de Boor, Elementary Numerical Analysis: An Algorithmic Approach , New York: McGraw-Hill, 1980.

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

Woodford, C., and C. Phillips, Numerical Methods with Worked Examples , London: Chapman and Hall, 1997.

The topic of finding roots is covered well in these books. See Chapters 5 and 6 in the Chapra book, Chapter 3 in the Conte book, and Chapter 2 in the Woodford book. The Chapra and Conte books discuss error analyses of the various root-finding algorithms. Conte also includes proofs of their convergence rates. Some of this chapter's example functions, especially the ones for fixed-point iteration, are from these books (some modified). See Section 3.1.4 in Atkinson and Chapter 25 in Scheid.