TR-2002017: Nearly Optimal Toeplitz/Hankel Computations
نویسنده
چکیده
منابع مشابه
TR-2002002: Can We Optimize Toeplitz/Hankel Computations? II. Singular Toeplitz/Hankel-like Case
In Part I, under the bit operation cost model we achieved nearly optimal randomized solution of nonsingular Toeplitz/Hankel linear system of equations based on Hensel's lifting. In Part II, we extend these results to the singular Toeplitz/Hankel-like case based on the MBA divide-and conquer algorithm and its combination with Hensel's lifting. We specify randomization and estimate the error/fail...
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Applying the superfast divide-and-conquer MBA algorithm for generally singular n × n Toeplitz-like or Hankel-like integer input matrices, we perform computations in the ring of integers modulo a power of a fixed prime, especially power of 2. This is practically faster than computing modulo a random prime but requires additional care to avoid degeneration, particularly at the stages of compressi...
متن کاملTR-2004013: Toeplitz and Hankel Meet Hensel and Newton: Nearly Optimal Algorithms and Their Practical Acceleration with Saturated Initialization
The classical and intensively studied problem of solving a Toeplitz/ Hankel linear system of equations is omnipresent in computations in sciences, engineering and signal processing. By assuming a nonsingular integer input matrix and relying on Hensel’s lifting, we compute the solution faster than with the divide-and-conquer algorithm by Morf 1974/1980 and Bitmead and Anderson 1980 and nearly re...
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The papers [MRT05], [CGS07], [XXG12], and [XXCB14] combine the techniques of the Fast Multipole Method of [GR87], [CGR98] with the transformations of matrix structures, traced back to [P90]. The resulting numerically stable algorithms approximate the solutions of Toeplitz, Hankel, Toeplitz-like, and Hankel-like linear systems of equations in nearly linear arithmetic time, versus the classical c...
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We seek the solution of banded, Toeplitz, Hankel, Vandermonde, Cauchy and other structured linear systems of equations with integer coefficients. By combining Hensel’s symbolic lifting with either divide-and-conquer algorithms or numerical iterative refinement, we unify the solution for all these structures. We yield the solution in nearly optimal randomized Boolean time, which covers both solu...
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