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dc.contributor.author전지현-
dc.creator전지현-
dc.date.accessioned2016-08-25T04:08:39Z-
dc.date.available2016-08-25T04:08:39Z-
dc.date.issued1997-
dc.identifier.otherOAK-000000023391-
dc.identifier.urihttp://dspace.ewha.ac.kr/handle/2015.oak/180739-
dc.identifier.urihttp://dcollection.ewha.ac.kr/jsp/common/DcLoOrgPer.jsp?sItemId=000000023391-
dc.description.abstractMany problems of mathematical physics are reducible to singular integral equations with Cauchy-type kernels. Of concern here are the Lobatto-Chebyshev formulae for the numerical solutions of singular integral equations of the Cauchy-type. Lobatto-Chebyshev quadrature at the extrema and the zeros of T_(n)(x) leads to an overdetermined system of linear algebraic equations. The coefficient matrix of the linear system of algebraic equations is shown to have an inverse, which is expressed in a neat, closed form. We show that the use of the zeros of T_(2n) as collocation yields well-conditioned coefficient matrix and good approximation to the exact solutions.;수학 물리학의 많은 문제들은 Cauchy 타입의 kernel을 가진 특이적분방정식으로 귀착된다. Cauchy타입의 특이적분방정식의 수치적 해를 구하기 위해서 Lobatto-Chebyshev 공식을 생각해 보기로 한다. T_(n)(x)의 극점들과 근들을 사용한 Lobatto-Chebyshev quadrature를 통해서 선형방정식들의 overdetermined 시스템이 얻어진다. 방정식의 선형시스템으로 이루어진 계수행렬은 잘 정리된 형태의 역행렬을 가진다. T_(2n)(x)의 근들을 collocation으로 사용할때 well- conditioned 계수행렬을 통해 정확한 해에 대한 좋은 근사 값을 가진다.-
dc.description.tableofcontentsTABLE OF CONTENTS = ⅰ ABSTRACT = ⅱ 1 INTRODUCTION = 1 2 DESCRETIZATION OF SINGULAR INTEGRAL EQUATIONS = 5 2.1 LOBATTO-CHEBYSHEV QUADRATURE = 5 2.2 IDENTITIES INVOLVING ZEROS OF CHEBYSHEV POLYNOMIALS = 11 2.2.1 IDENTITIES WITH ZEROS OF T_(n)(x) AND U_(n-1)(x) = 11 2.2.2 IDENTITIES WITH ZEROS OF T_(2n)(x) AND U_(2n-1)(x) = 12 3 INVERSE MATRIX AND NORMS = 13 3.1 GENERALIZED INVERSE OF A = 13 3.2 NORMS OF MATRICES = 14 4 CONVERGENCE RESULTS = 20 5 NUMERICAL RESULTS = 23 References = 29 논문초록 = 31-
dc.formatapplication/pdf-
dc.format.extent755551 bytes-
dc.languageeng-
dc.publisherThe Graduate School, Ewha Womans University-
dc.subjectNumerical solution-
dc.subjectLobatto Chebyshev-
dc.subjectoverdetermined-
dc.titleNumerical solutions of S.I.E. using Lobatto-Chebyshev quadrature and overdetermined systems-
dc.typeMaster's Thesis-
dc.format.pageii, 31 p.-
dc.identifier.thesisdegreeMaster-
dc.identifier.major대학원 수학과-
dc.date.awarded1998. 2-
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