کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
697691 890379 2009 8 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Fast computation of smoothing splines subject to equality constraints
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی کنترل و سیستم های مهندسی
پیش نمایش صفحه اول مقاله
Fast computation of smoothing splines subject to equality constraints
چکیده انگلیسی

The issue of constructing periodic smoothing splines has been recently formulated as a controlled two point boundary value problem which admits a state-space description. In the context of minimum norm problems in Hilbert spaces, it has been shown that the solution is the sum of a finite number of basis functions and can be obtained with a number of operations which scales with the cube of the sum of the number of measurements and boundary constraints. In this paper we consider a more general class of variational problems subject to equality constraints which contains the periodic smoothing spline problem as a special case. Using the theory of reproducing kernel Hilbert spaces we derive a solution to the problem which has the same computational complexity as that recently proposed. Next, assuming that the problem admits a state-space representation, we obtain an algorithm whose complexity is linear in the number of measurements. We also show that the solution of the problem admits the structure of a particular regularization network whose weights can be computed in linear time. Closed form expressions for the basis functions associated with the periodic cubic smoothing spline problem are finally derived.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Automatica - Volume 45, Issue 12, December 2009, Pages 2842–2849
نویسندگان
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