6.006 Introduction to Algorithms (Fall 2011, MIT OCW). Taught by Professor Erik Demaine and Professor Srinivas Devadas, this course provides an introduction to mathematical modeling of computational problems. It covers the common algorithms, algorithmic paradigms, and data structures used to solve these problems. The course emphasizes the relationship between algorithms and programming, and introduces basic performance measures and analysis techniques for these problems.
(from ocw.mit.edu)
Lecture 12 - Square Roots, Newton's Method
This lecture begins with error analysis of Newton's method and a comparison of multiplication algorithms. It then covers high-precision division, which is required for Newton's method, and discusses the complexity of division and computing square roots.