This chapter is concerned with “numerical methods” of linear algebra, an area of study that encompasses techniques for solving large-scale linear systems and for finding numerical approximations of various kinds. It is not our objective to discuss algorithms and technical issues in fine detail since there are many excellent books on the subject. Rather, we will be concerned with introducing some of the basic ideas and exploring two important contemporary applications that rely heavily on numerical ideas—singular value decomposition and data compression. A computing utility such as MATLAB, Mathematica, or Maple is recommended for Sections 9.2 to 9.5.
9.1 LU-Decompositions
Solving ...
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