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Applied Mathematical Methods by Bhaskar Dasgupta

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6

Special Systems and Special Methods

Even though the methods descrbied in the previous two chapters have wide applications, situations do arise when the linear system possesses certain special structure or some additional information can be obtained by tapping the domain knowledge of the application area. If the problem size is large, then the exploitation of these aspects becomes vital from the viewpoint of efficiency, if not effectiveness. Starting from the concept of quadratic forms, this chapter provides a bird’s-eye view of symmetry, positive definiteness and sparsity issues, including their use in enhancing computational efficiency.

Quadratic Forms, Symmetry and Positive Definiteness

A homogeneous second degree scalar function of a vector ...

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