Invertibility of a tridiagonal operator with an application to a non-uniform sampling problem

Let T be a tridiagonal operator on which has strict row and column dominant property except for some finite number of rows and columns. This matrix is shown to be invertible under certain conditions. This result is also extended to double infinite tridiagonal matrices. Further, a general theorem is...

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Bibliographic Details
Published inLinear & multilinear algebra Vol. 65; no. 5; pp. 973 - 990
Main Authors Antony Selvan, A., Radha, R.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 04.05.2017
Taylor & Francis Ltd
Subjects
Algebra
Diagonal dominance
finite-dimensional truncation
LU-decomposition
Mathematical analysis
Operators
Operators (mathematics)
Primary: 47B37
Sampling
Secondary: 15A60
shift-invariant space
stable set of sampling
Theorems
tridiagonal operator
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Summary:Let T be a tridiagonal operator on which has strict row and column dominant property except for some finite number of rows and columns. This matrix is shown to be invertible under certain conditions. This result is also extended to double infinite tridiagonal matrices. Further, a general theorem is proved for solving an operator equation using its finite-dimensional truncations, where T is a double infinite tridiagonal operator. Finally, it is also shown that these results can be applied in order to obtain a stable set of sampling for a shift-invariant space.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2016.1217978