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Applied Mathematical Methods by Bhaskar Dasgupta

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12

QR Decomposition Method

QR decomposition is the most effective method discovered so far for solving the algebraic eigenvalue problem. In this chapter, we study the meaning and methods of the decomposition, and also its use in the eigenvalue problem. In one section, we also try to scale some of the theoretical ‘how and why’ of the method. Finally, we make a foray into the sophisticated strategy of shift, with special emphasis on the important case of symmetric tridiagonal matrices.

QR Decomposition

In the two previous chapters, we have studied methods of the eigenvalue problem based on rotation and reflection transformations. The third kind of methods for finding out appropriate similarity transformations are based on matrix decomposition. ...

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