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Mathematics of Computation

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A general orthogonalization technique with applications to time series analysis and signal processing


Author: George Cybenko
Journal: Math. Comp. 40 (1983), 323-336
MSC: Primary 65F25; Secondary 62M20
DOI: https://doi.org/10.1090/S0025-5718-1983-0679449-6
MathSciNet review: 679449
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Abstract: A new orthogonalization technique is presented for computing the QR factorization of a general $ n \times p$ matrix of full rank $ p\,(n \geqslant p)$. The method is based on the use of projections to solve increasingly larger subproblems recursively and has an $ O(n{p^2})$ operation count for general matrices. The technique is readily adaptable to solving linear least-squares problems. If the initial matrix has a circulant structure the algorithm simplifies significantly and gives the so-called lattice algorithm for solving linear prediction problems. From this point of view it is seen that the lattice algorithm is really an efficient way of solving specially structured least-squares problems by orthogonalization as opposed to solving the normal equations by fast Toeplitz algorithms.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1983-0679449-6
Keywords: Orthogonalization, least-squares problems, linear prediction
Article copyright: © Copyright 1983 American Mathematical Society