TR-2004009: A Reduction of the Matrix Eigenproblem to Polynomial Rootfinding via Similarity Transforms into Arrow-Head Matrices
نویسنده
چکیده
We modify the customary approach to solving the algebraic eigenproblem. Instead of applying the QR algorithm to a Hessenberg matrix, we begin with the recent unitary similarity transform into a triangular plus rank-one matrix. Our novelty is nonunitary transforms of this matrix into similar arrow-head matrices, which we perform at a low arithmetic cost. The resulting eigenproblem can be effectively solved by the known algorithms. We also outline some directions for further work.
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تاریخ انتشار 2016