http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
- 中文 을 입력하시려면 zhongwen을 입력하시고 space를누르시면됩니다.
- 北京 을 입력하시려면 beijing을 입력하시고 space를 누르시면 됩니다.
RISS 인기검색어
- 검색키워드
- 저자 : Micchelli, (검색결과 2 건)
- 무료
- 기관 내 무료
- 유료
-
On multivariate discrete least squares
Lee, Y.J.,Micchelli, C.A.,Yoon, J. Academic Press 2016 Journal of approximation theory Vol.211 No.-
<P>For a positive integer n is an element of N we introduce the index set N-n := {1, 2,..., n}. Let X := {x(i) : i is an element of N-n} be a distinct set of vectors in R-d, Y := {y(i) : i is an element of N-n} a prescribed data set of real numbers in R and F := {f(j) : j is an element of N-m}, m < n, a given set of real valued continuous functions defined on some neighborhood O of R-d containing X. The discrete least squares problem determines a (generally unique) function f = Sigma(j is an element of Nm) c(j)(star) f(j) is an element of spanF which minimizes the square of the l(2)-norm Sigma(i is an element of Nn) (Sigma(j is an element of Nm) c(j)f(j)(x(i)) - y(i))(2) over all vectors (c(j) : j is an element of N-m) is an element of R-m. The value of f at some s is an element of O may be viewed as the optimally predicted value (in the l(2)-sense) of all functions in spanF from the given data X = {x(i) : i is an element of N-n} and Y = {y(i) : i is an element of N-n}. We ask 'What happens if the components of X and s are nearly the same'. For example, when all these vectors are near the origin in R-d. From a practical point of view this problem comes up in image analysis when we wish to obtain a new pixel value from nearby available pixel values as was done in [2], for a specified set of functions F. This problem was satisfactorily solved in the univariate case in Section 6 of Lee and Micchelli (2013). Here, we treat the significantly more difficult multivariate case using an approach recently provided in Yeon Ju Lee, Charles A. Micchelli and Jungho Yoon (2015). (C) 2016 Published by Elsevier Inc.</P>
-
A study on multivariate interpolation by increasingly flat kernel functions
Lee, Yeon Ju,Micchelli, Charles A.,Yoon, Jungho Elsevier 2015 Journal of mathematical analysis and applications Vol.427 No.1
<P><B>Abstract</B></P> <P>In this paper, we improve upon some observations made in recent papers on the subject of increasingly flat interpolation. We shall establish that the corresponding Lagrange functions converge both for a finite set of functions (collocation matrix) and also for kernels (Fredholm matrix). In our analysis, we use a finite Maclaurin expansion of a multivariate function with remainder and some additional matrix theoretic facts.</P>
연관 검색어 추천
이 검색어로 많이 본 자료
활용도 높은 자료
