کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
469951 698373 2008 6 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Eigen-solving via reduction to DPR1 matrices
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر علوم کامپیوتر (عمومی)
پیش نمایش صفحه اول مقاله
Eigen-solving via reduction to DPR1 matrices
چکیده انگلیسی

Highly effective polynomial root-finders have been recently designed based on eigen-solving for DPR1 (that is diagonal + rank-one) matrices. We extend these algorithms to eigen-solving for the general matrix by reducing the problem to the case of the DPR1 input via intermediate transition to a TPR1 (that is triangular + rank-one) matrix. Our transforms use substantially fewer arithmetic operations than the QR classical algorithms but employ non-unitary similarity transforms of a TPR1 matrix, whose representation tends to be numerically unstable. We, however, operate with TPR1 matrices implicitly, as with the inverses of Hessenberg matrices. In this way our transform of an input matrix into a similar DPR1 matrix partly avoids numerical stability problems and still substantially decreases arithmetic cost versus the QR algorithm.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computers & Mathematics with Applications - Volume 56, Issue 1, July 2008, Pages 166–171
نویسندگان
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