Parallel solution of certain toeplitz linear systems
SIAM Journal on Computing
Polynomial division and its computational complexity
Journal of Complexity
Optimal size integer division circuits
SIAM Journal on Computing
Polynomial division with a remainder by means of evaluation and interpolation
Information Processing Letters
Improved parallel polynomial division
SIAM Journal on Computing
Polynomial and matrix computations (vol. 1): fundamental algorithms
Polynomial and matrix computations (vol. 1): fundamental algorithms
Variations on computing reciprocals of power series
Information Processing Letters - Special issue analytical theory of fuzzy control with applications
Structured matrices and polynomials: unified superfast algorithms
Structured matrices and polynomials: unified superfast algorithms
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
A New Approach to Resultant Computations and Other Algorithms with Exact Division
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
Modern Computer Algebra
Newton's method and FFT trading
Journal of Symbolic Computation
Superfast solution of linear convolutional Volterra equations using QTT approximation
Journal of Computational and Applied Mathematics
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Computing the reciprocal of a polynomial in z modulo a power zn is well known to be closely linked to polynomial division and equivalent to the inversion of an n × n triangular Toeplitz matrix. The degree k of the polynomial is precisely the bandwidth of the matrix, and so the matrix is banded iff k ≪ n. We employ the above equivalence and some elementary but novel and nontrivial techniques to obtain minor yet noticeable acceleration of the solution of the cited fundamental computational problems.