Superfast Solution of Real Positive Definite Toeplitz Systems
نویسندگان
چکیده
منابع مشابه
Superfast Solution of Real Positive Definite Toeplitz Systems
Abstract. We describe an implementation of the generalized Schur algorithm for the superfast solution of real positive definite Toeplitz systems of order n + 1, where n = 2ν . Our implementation uses the split-radix fast Fourier transform algorithms for real data of Duhamel. We are able to obtain the nth Szegő polynomial using fewer than 8n log 2 n real arithmetic operations without explicit us...
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We present a new superfast algorithm for solving Toeplitz systems. This algorithm is based on a relation between the solution of such problems and syzygies of polynomials or moving lines. We show an explicit connection between the generators of a Toeplitz matrix and the generators of the corresponding module of syzygies. We show that this module is generated by two elements and the solution of ...
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In this paper we are concerned with the solution of n × n Hermitian Toeplitz systems with nonnegative generating functions f . The preconditioned conjugate gradient (PCG) method with the well–known circulant preconditioners fails in the case where f has zeros. In this paper we consider as preconditioners band–Toeplitz matrices generated by trigonometric polynomials g of fixed degree l. We use d...
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A new superfast O(n log n) complexity direct solver for real symmetric Toeplitz systems is presented. The algorithm is based on 1. the reduction to symmetric right-hand sides, 2. a polynomial interpretation in terms of Chebyshev polynomials, 3. an inversion formula involving real trigonometric transformations, and 4. an interpretation of the equations as a tangential interpolation problem. The ...
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 1988
ISSN: 0895-4798,1095-7162
DOI: 10.1137/0609005