Iterative Linear Algebra

This chapter describes iterative methods for approximately solving systems of linear equations. This discussion begins by presenting the concept of a sparse matrix, where it arises and how it might be represented in a computer. Next, simple methods based on iterative improvement are presented, along with termination criteria for the iteration. Afterwards, more elaborate gradient methods are examined, such as conjugate gradients and biconjugate gradients. The chapter proceeds tominimum resiual methods, and ends with a fairly detailed discussion of multigrid methods.

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