Chapter 12. Matrices and QR decomposition
This chapter covers
From physics and engineering to economics and sociology, there is no getting away from matrices. These mathematical structures can represent systems of equations, statistical data, DNA sequences, and the distribution of stresses within an object. Matrices have been used to structure data for centuries, and new applications appear on a regular basis.
Just as there are many uses for matrices, there are also many different ways to analyze them. But not all matrices are easy to work with. Mathematicians frequently find it necessary to factor a disordered matrix into matrices that are easy to analyze, and then perform their operations on the factors. This factorization is conceptually similar to factoring an integer into its prime divisors or factoring a polynomial into its roots.
One of the most popular methods of factoring a matrix is called the QR decomposition. This factors a matrix into two matrices whose qualities make them simple to analyze and manipulate. The goal of this chapter is to explain the theory behind QR decomposition and show how it can be implemented with OpenCL.