Superfast Solution of Real Positive Definite Toeplitz Systems
نویسندگان
چکیده
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 use of the bit-reversal permutation. Since Levinson’s algorithm requires slightly more than 2n operations to obtain this polynomial, we achieve crossover with Levinson’s algorithm at n = 256.
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