Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4600976 | Linear Algebra and its Applications | 2011 | 29 Pages |
Abstract
Let J be a monic Jacobi matrix associated with the Cauchy transform F of a probability measure. We construct a pair of the lower and upper triangular block matrices L and U such that J=LU and the matrix JC=UL is a monic generalized Jacobi matrix associated with the function FC(λ)=λF(λ)+1. It turns out that the Christoffel transformation JC of a bounded monic Jacobi matrix J can be unbounded. This phenomenon is shown to be related to the effect of accumulating at ∞ of the poles of the Padé approximants of the function FC although FC is holomorphic at ∞. The case of the UL-factorization of J is considered as well.
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Physical Sciences and Engineering
Mathematics
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