Toeplitz matrices with banded inverses |
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Authors: | Wayne W Barrett |
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Institution: | Department of Mathematics Brigham Young University Provo, Utah 84602, USA |
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Abstract: | Given a Toeplitz matrix T with banded inverse i.e., (T?1)ij=0 for j?i>p], we show that the elements of T can be expressed in terms of the roots of a polynomial. Then, using properties we have previously established, we generalize this result appropriately to allow singular T and show that the converse also holds. Finally, we give a sufficient condition for the decay of the elements of T as one moves away from the diagonal. |
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