Full metadata record
DC Field | Value | Language |
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dc.contributor.author | 윤정호 | * |
dc.date.accessioned | 2016-09-08T03:09:38Z | - |
dc.date.available | 2016-09-08T03:09:38Z | - |
dc.date.issued | 2016 | * |
dc.identifier.issn | 0021-9045 | * |
dc.identifier.other | OAK-19229 | * |
dc.identifier.uri | https://dspace.ewha.ac.kr/handle/2015.oak/232167 | - |
dc.description.abstract | For a positive integer n∈N we introduce the index set Nn:={1,2,…,n}. Let X:={xi:i∈Nn} be a distinct set of vectors in Rd, Y:={yi:i∈Nn} a prescribed data set of real numbers in R and F:={fj:j∈Nm},m<n, a given set of real valued continuous functions defined on some neighborhood O of Rd containing X. The discrete least squares problem determines a (generally unique) function f=∑j∈Nmcj ⋆fj∈spanF which minimizes the square of the ℓ2−norm ∑i∈Nn(∑j∈Nmcjfj(xi)−yi)2 over all vectors (cj:j∈Nm)∈Rm. The value of f at some s∈O may be viewed as the optimally predicted value (in the ℓ2−sense) of all functions in spanF from the given data X={xi:i∈Nn} and Y={yi:i∈Nn}. 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 Rd. 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). © 2016 | * |
dc.language | English | * |
dc.publisher | Academic Press Inc. | * |
dc.subject | Collocation matrix | * |
dc.subject | Multivariate least squares | * |
dc.subject | Multivariate Maclaurin expansion | * |
dc.subject | Wronskian | * |
dc.title | On multivariate discrete least squares | * |
dc.type | Article | * |
dc.relation.volume | 211 | * |
dc.relation.index | SCIE | * |
dc.relation.index | SCOPUS | * |
dc.relation.startpage | 78 | * |
dc.relation.lastpage | 84 | * |
dc.relation.journaltitle | Journal of Approximation Theory | * |
dc.identifier.doi | 10.1016/j.jat.2016.07.005 | * |
dc.identifier.wosid | WOS:000384954300006 | * |
dc.identifier.scopusid | 2-s2.0-84982124217 | * |
dc.author.google | Lee Y.J. | * |
dc.author.google | Micchelli C.A. | * |
dc.author.google | Yoon J. | * |
dc.contributor.scopusid | 윤정호(57221276460) | * |
dc.date.modifydate | 20240118161402 | * |