A backward three-term recurrence relation for vector valued continued fractions and its applications

This paper presents a backward three-term recurrence relation, which is a solution of an open problem in Graves-Morris (Numer. Math. 42 (1983) 331). By means of this relation, we succeed in establishing some conclusions about the two backward successive convergents of vector valued continued fractio...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 142; no. 2; pp. 389 - 400
Main Authors Zhao, Huan-xi, Zhu, Gong-qin, Xiao, Ping
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 15.05.2002
Elsevier
Subjects
Approximations and expansions
Backward three-term recurrence relation
Convergence
Exact sciences and technology
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Numerical linear algebra
Sciences and techniques of general use
Vector valued continued fraction
Vector valued continued fraction
65D05
Backward three-term recurrence relation
41A20
65F30
Convergence
Numerical method
Approximation
Recurrence relation
Continued fractions
Linear algebra
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Summary:This paper presents a backward three-term recurrence relation, which is a solution of an open problem in Graves-Morris (Numer. Math. 42 (1983) 331). By means of this relation, we succeed in establishing some conclusions about the two backward successive convergents of vector valued continued fractions. Moreover, an expression for the vector valued continued fraction in series form is obtained and some theorems of the convergence of the vector valued continued fraction are proved by virtue of the recurrence relation.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0377-0427
1879-1778
DOI:10.1016/S0377-0427(01)00419-8