The inverse of a totally positive biinfinite band matrix
Author:
Carl de Boor
Journal:
Trans. Amer. Math. Soc. 274 (1982), 4558
MSC:
Primary 47B37; Secondary 15A09
MathSciNet review:
670917
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Abstract: It is shown that a bounded biinfinite banded totally positive matrix is boundedly invertible iff there is one and only one bounded sequence mapped by to the sequence . The argument shows that such a matrix has a main diagonal, i.e., the inverse of is the bounded pointwise limit of inverses of finite sections of principal with respect to a particular diagonal; hence or its inverse is again totally positive.
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 C. de Boor, What is the main diagonal of a biifinite band matrix?, MRC TSR 2049 (1980); in [5,1123].
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 , Dichotomies for band matrices, MRC TSR 2057 (1980); SIAM J. Numer. Anal. 17 (1980), 894907. MR 595452 (83g:41010)
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 C. de Boor, S. Friedland and A. Pinkus, Inverses of infinite sign regular matrices, MRC TSR 2159 (1980); Trans. Amer. Math. Soc. 274 (1982), 5968. MR 670918 (84f:47035b)
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 R. DeVore and K. Scherer (eds.). Quantitative approximation, Academic Press, New York, 1980. MR 588164 (81i:41001)
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 S. Karlin, Total positivity. I, Stanford University Press, Stanford, Calif., 1968. MR 0230102 (37:5667)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947198206709175
PII:
S 00029947(1982)06709175
Keywords:
Biinfinite,
matrix,
total positivity,
inverse,
banded,
main diagonal
Article copyright:
© Copyright 1982
American Mathematical Society
