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The operators \pi_G of best approximations and continuous metric projections
Hyang Joo Rhee 한국전산응용수학회 2022 Journal of applied mathematics & informatics Vol.40 No.3
In this paper, we shall consider some properties of the metric projection as a set valued mapping. For a set G in a metric space E, the mapping \pi_G ; x \rightarrow \pi_G(x) of E into 2^G is called set valued metric projection of E onto G. We investigated the properties related to the projection P_{S(\cdot)}(\cdot) and \pi_{S(\cdot)}(\cdot) as one-sided best simultaneous approximations.
템플릿 패킹 문제에 대한 최적-적합 전략을 사용한 근사 알고리즘
권오흠,송하주 한국차세대컴퓨팅학회 2016 한국차세대컴퓨팅학회 논문지 Vol.12 No.3
이 논문에서는 서로 다른 종류의 아이템들을 생산하기 위해서 필요한 템플릿을 구성하는 것과 관련된 일종의 패킹문제를 다룬다. 고정된 개수의 아이템이 배치된 하나 혹은 그 이상의 템플릿을 반복 인쇄함으로써 요구된 수량의 아이템들을 생산한다. 문제의 목적은 초과 생산량이 최소가 되도록 아이템들을 템플릿에 배치하는 것이다. 이 문제는NP-hard임이 밝혀져 있으며, 탐욕적 기법과 분기한정법에 기반한 근사 알고리즘이 알려져 있다. 본 논문에서는 이문제를 해결하기 위하여 잘 알려진 최적-적합 전략을 이용한 또 다른 다항시간 근사 알고리즘을 제시한다. 다양한실험 데이터를 통해 제시한 알고리즘의 성능을 평가하였으며 선행 연구에서 제시된 알고리즘과 비교하였다. This paper deals with a kind of packing problem of which the goal is to compose one or more templates which will be used to produce the items of different types. Each template consists of a fixed number of slots which are assigned to the item types and the production of the items is accomplished by printing the template repeatedly. The objective is to minimize the total number of produced items. This problem is known to be NP-hard. Approximation algorithms based on either greedy approach or branch-and-bound technique have been proposed. We present another polynomial time approximation algorithm based on the well-known best-fit strategy. We perform experiments to compare the performance of the proposed algorithm with the previous ones.
S. K. Sen,R. P. Agarwal,G. A. Shaykhian 장전수학회 2009 Advanced Studies in Contemporary Mathematics Vol.19 No.1
A k-digit rational approximation of an irrational number is defined as the rational number with k digits in the numerator. The actual best k digit rational approximation is unique and is the true/absolute one. The best k - digit rational approximation, when it exists, obtained from the convergents of the continued fraction representation of an irrational number is also unique and need not be the same as the absolute one. The best k digit decimal number for the irrational number is also unique but is not the true best k - digit rational approximation, in general. We discuss here the quality implying error, the cost implying computational/time complexity, and scope implying a possible usage/application of the concerned three computational algorithms.
Strongly Unique Best Coapproximation
RAO, GEETHA S.,SARAVANAN, R. Department of Mathematics 2003 Kyungpook mathematical journal Vol.43 No.4
This paper delineates some fundamental properties of the set of strongly unique best coapproximation. Uniqueness of strongly unique best coapproximation is studied. Some characterizations of strongly unique best coapproximation and strongly unique best approximation are obtained. Some more results concerning strongly unique best uniform coapproximation and strongly unique best uniform approximation are presented. Some relations between best uniform approximation and strongly unique best uniform coapproximation are established.
A STUDY ON TYPES OF APPROXIMATION IN THE SENSE OF 2-STRUCTURES
MEHMET AÇIKGÖZ,YUSUF KARAKUS,DOGAN DÖNMEZ 장전수학회 2011 Proceedings of the Jangjeon mathematical society Vol.14 No.1
The problem of approximation and best approximation has been studied by many mathematicians. Most of works have dealt with the existence,uniqueness and characterization of approximation and best approximations in spaces of continuous functions with values in Banach spaces. But little or no work on approximation has been done in the sense of 2-structures such 2-normed sapaces, generalized 2-normed spaces and 2-Banach spaces. The aim of this paper is to give the types of approximation and investigate the approx-imation in the sense of these spaces. In addition, we shall give some results and related examples on the sets of approximation and coapproximation.
Common fixed point theorem and invariant approximation in complete linear metric spaces
Hemant Kumar Nashine 영남수학회 2012 East Asian mathematical journal Vol.28 No.5
A common fixed point result of Gregus type for subcompati- ble mappings defined on a complete linear metric space is obtained. The considered underlying space is generalized from Banach space to complete linear metric spaces, which include Banach space and complete metriz- able locally convex spaces. Invariant approximation results have also been determined as its application
EXPANSION THEORY FOR THE TWO-SIDED BEST SIMULTANEOUS APPROXIMATIONS
RHEE, HYANG JOO The Korean Society for Computational and Applied M 2021 Journal of applied mathematics & informatics Vol.39 No.3
In this paper, we study the characterizations of two-sided best simultaneous approximations for ℓ-tuple subset from a closed convex subset of ℝ<sup>m</sup> with ℓ<sup>m</sup><sub>1</sub>(w)-norm. Main fact is, k<sup>*</sup> is a two-sided best simultaneous approximation to F from K if and only if there exist f<sub>1</sub>, …, f<sub>p</sub> in F, for any k ∈ K $${\mid}{\sum\limits_{i=1}^{m}}sgn(f_{ji}-k^*_i)k_iw_i{\mid}{\leq}\;{\sum\limits_{i{\in}Z(f_j-k^*)}}\;{\mid}k_i{\mid}w_i$$ for each j = 1, …, p and 𝐰 ∈ W.
The best simultaneous approximation in linear 2-normed spaces
mehmetacikgoz 장전수학회 2012 Proceedings of the Jangjeon mathematical society Vol.15 No.4
In this paper, we shall investigate and analyse a new study on the best simultaneous approximation in the context of linear 2-normed spaces inspired by Elumalai and his coworkers in [10]. The basis of this investigation is to extend and re nement the de nition of the classical aproximation, best approximation and some related concepts to linear 2-normed spaces.
BEST APPROXIMATION SETS IN LINEAR 2-NORMED SPACES
Elumalai, S.,Cho, Y.J.,Kim, S.S Korean Mathematical Society 1997 대한수학회논문집 Vol.12 No.3
In this paper, we give some properties of the sets $D_z(x_o, G)P_{G, z}(x)$. We also provide the relation between $P_{G, z}(x)$ and G$\hat{a}$teaux derivatives.
One-sided best simultaneous $L_1$-approximation for a compact set
Park, Sung-Ho,Rhee, Hyang-Joo Korean Mathematical Society 1998 대한수학회보 Vol.35 No.1
In this paper, we discuss the characterizations and uniqueness of a one-sided best simultaneous approximation for a compact subset from a convex subset of a finite-dimensional subspace of a normed linear space $C_1(X)$. The motivation is furnished by the characterizations of the one-sided best simultaneous approximations for a finite subset ${f_1, \ldots, f_\ell}$ for any $\ell \in N$.