Generalized Givens Transformation and its Application ∗
نویسنده
چکیده
Abstract A new transformation, a generalization of the Givens rotation, is introduced here. Its properties are studied. As application of the new transformation, we discuss how to employ it to tridiagonalize matrices similarly, without requiring an intermediate transformation to Hessenberg form. This approach to tridiagonalization is cheaper than usual strategies, specially for sparse case in the absence of breakdown. Some implementation issues, including partial pivoting technique, are discussed too. Numerical examples illustrate that the new tridiagonalization works quite well whenever it has no breakdown.
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