Orthogonal Factorization and Linear Least Squares Problems

Abstract

Orthogonal factorization (or QR factorization) of a dense matrix is an essential tool in several matrix computations. In this chapter we consider algorithms for QR as well as its application to the solution of linear least squares problems. The QR factorization is also a major step in some methods for computing eigenvalues; cf. Chap. 8. Algorithms for both the QR factorization and the solution of linear least squares problems are major components in data analysis and areas such as computational statistics, data mining and machine learning; cf. [1][2][3].