On the Berlekamp/Massey algorithm and counting singular Hankel matrices over a finite field
- MathematicsJ. Symb. Comput.
Linear Algebra for Computing Gröbner Bases of Linear Recursive Multidimensional Sequences
- Computer ScienceJ. Symb. Comput.
An FGLM-like algorithm for finding the relations in the table is produced, which lets us use linear algebra techniques and make use of fast structured linear algebra similarly to the Hankel interpretation of Berlekamp--Massey.
In-depth comparison of the Berlekamp - Massey - Sakata and the Scalar-FGLM algorithms: the non adaptive variants
- Computer ScienceJ. Symb. Comput.
Fast estimates of Hankel matrix condition numbers and numeric sparse interpolation
- MathematicsSNC '11
It is demonstrated by experiments that the Gohberg-Semencul formula for the inverse of a Hankel matrix to compute estimates for the structured condition numbers of all arising Hankel matrices in quadratic arithmetic time overall lead to a viable termination criterion for polynomials with about 20 non-zero terms and of degree about 100, even in the presence of noise of relative magnitude 10-5.
Common Factors in Fraction-Free Matrix Decompositions
- MathematicsMath. Comput. Sci.
It is shown that fraction-free Gauß–Bareiss reduction leads to triangular matrices having a non-trivial number of common row factors in theLUandQRmatrix decompositions using exact computations.
Sparse Polynomial Hermite Interpolation
- Computer Science, MathematicsISSAC
These algorithms generalize to multivariate polynomials, higher derivatives and sparsity with respect to Chebyshev polynomial bases, and have algorithms that can correct errors in the points by oversampling at a limited number of good values.
Numerical Sparsity Determination and Early Termination
- Computer ScienceISSAC
An algorithm is given that can be used to compute the sparsity and estimate the minimal number of samples needed in numerical sparse interpolation and the early termination strategy of polynomial interpolation has been incorporated in the algorithm.
On the matrix feedback shift register synthesis for matrix sequences
- Computer ScienceScience China Information Sciences
In this paper, a generalization of the linear feedback shift register synthesis problem is presented for synthesizing minimum-length matrix feedback shift registers (MFSRs for short) to generate…
Sparse Interpolation With Errors in Chebyshev Basis Beyond Redundant-Block Decoding
- Computer ScienceIEEE Transactions on Information Theory
Sparse interpolation algorithms for recovering a polynomial with LaTeX terms from inline-formula evaluations at distinct values for the variable with Chebyshev Basis, which return a list of valid sparse interpolants for the algorithm.
Sparse Polynomial Interpolation and Testing
- Computer Science
Two methods for the interpolation of a sparse polynomial modelled by a straight-line program (SLP): a sequence of arithmetic instructions and an alternative method of randomized Kronecker substitutions that can more efficiently reconstruct a sparse interpolant f from multiple univariate images of considerably reduced degree.
SHOWING 1-10 OF 29 REFERENCES
On the matrix berlekamp-massey algorithm
- Computer ScienceTALG
This work analyzes the Matrix Berlekamp/Massey algorithm and gives new proofs of correctness and complexity for the algorithm, which is based on self-contained loop invariants and includes an explicit termination criterion for a given determinantal degree bound of the minimal matrix generator.
Algorithms for computing the sparsest shifts of polynomials via the Berlekamp/Massey algorithm
- Computer ScienceISSAC '02
A fraction-free version of the Berlekamp/Massey algorithm is given, which does not require rational numbers or functions and GCD operations on the arising numerators and denominators and is more efficient than the classical extended Euclidean algorithm.
A minimal realization algorithm for matrix sequences
- Computer Science, MathematicsCDC 1973
We give an algorithm for solving the Pade approximation problem for matrix sequences over an arbitrary field. The algorithm is a multivariate version of one first proposed by Berlekamp and Massey in…
Fraction-free computation of matrix Padé systems
- Mathematics, Computer ScienceISSAC
A fraction-free approach to the computation of matrix Pad& systems by determining a modified Schur complement for the coefficient matrices of the linear systems of equations that are associated to matrix Pad &approximation problems.
Solving homogeneous linear equations over GF (2) via block Wiedemann algorithm
- Computer Science
A method of solving large sparse systems of homogeneous linear equations over G F ( 2 ) , the field with two elements, is proposed and an algorithm due to Wiedemann is modified, which is competitive with structured Gaussian elimination in terms of time and has much lower space requirements.
Algebraic coding theory
- Computer ScienceMcGraw-Hill series in systems science
This is the revised edition of Berlekamp's famous book, "Algebraic Coding Theory," originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering…
On Euclid's Algorithm and the Theory of Subresultants
An elementary treatment of the theory of subresultants is presented, and the relationship of the sub resultants of a given pair of polynomials to their polynomial remainder sequence as determined by Euclid's algorithm is examined.
Fraction-Free Computation of Matrix Rational Interpolants and Matrix GCDs
- Mathematics, Computer ScienceSIAM J. Matrix Anal. Appl.
A new set of algorithms for computation of matrix rational interpolants and one-sided matrix greatest common divisors, suitable for computation in exact arithmetic domains where growth of coefficients in intermediate computations is a central concern.
On Euclid's algorithm and the computation of polynomial greatest common divisors
- Computer Science, MathematicsSYMSAC '71
This paper examines the computation of polynomial greatest common divisors by various generalizations of Euclid's algorithm, and it is shown that the modular algorithm is markedly superior.
Sylvester’s identity and multistep integer-preserving Gaussian elimination
A method is developed which permits integer-preserving elimination in systems of linear equations, AX = B, such that (a) the magnitudes of the coefficients in the transformed matrices are minimized,…