کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
755690 1462624 2015 19 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Stochastic algorithms for solving structured low-rank matrix approximation problems
ترجمه فارسی عنوان
الگوریتم های تصادفی برای حل مسائل تقریبی ماتریس پایین رتبه بندی ساختار یافته
کلمات کلیدی
تقریبی پایین ساختاری، ماتریکس هانکل، بهینه سازی جهانی
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی مکانیک
چکیده انگلیسی


• The structured low rank approximation problem is rigorously studied.
• Globally convergent stochastic algorithms are provided for the Hankel structured low rank approximation problem.
• Examples and simulations demonstrating the value of the proposed methodology are included.

In this paper, we investigate the complexity of the numerical construction of the Hankel structured low-rank approximation (HSLRA) problem, and develop a family of algorithms to solve this problem. Briefly, HSLRA is the problem of finding the closest (in some pre-defined norm) rank r approximation of a given Hankel matrix, which is also of Hankel structure. We demonstrate that finding optimal solutions of this problem is very hard. For example, we argue that if HSLRA is considered as a problem of estimating parameters of damped sinusoids, then the associated optimization problem is basically unsolvable. We discuss what is known as the orthogonality condition, which solutions to the HSLRA problem should satisfy, and describe how any approximation may be corrected to achieve this orthogonality. Unlike many other methods described in the literature the family of algorithms we propose has the property of guaranteed convergence.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Communications in Nonlinear Science and Numerical Simulation - Volume 21, Issues 1–3, April 2015, Pages 70–88
نویسندگان
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