Computation of the Newton step for the even and odd characteristic polynomials of a symmetric positive definite Toeplitz matrix |
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Authors: | A Melman |
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Institution: | Department of Applied Mathematics, School of Engineering, Santa Clara University, Santa Clara, California 95053 |
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Abstract: | We compute the Newton step for the characteristic polynomial and for the even and odd characteristic polynomials of a symmetric positive definite Toeplitz matrix as the reciprocal of the trace of an appropriate matrix. We show that, after the Yule-Walker equations are solved, this trace can be computed in additional arithmetic operations, which is in contrast to existing methods, which rely on a recursion, requiring additional arithmetic operations. |
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Keywords: | Toeplitz matrix even odd eigenvalue characteristic polynomial Newton's method |
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