Results 21 to 30 of about 94,123 (313)
Polynomial decomposition algorithms
Journal of Symbolic Computation, 1985 \textit{M. Fried} and \textit{R. MacRae} [Math. Ann. 180, 220--226 (1969; Zbl 0185.28803)] proved the following theorem: Let \(f,g,p,q\) be univariate polynomials over an arbitrary field \(k\). Then \(p(x)-q(z)\) divides \(f(x)-g(z)\) if and only if there exists a polynomial \(F(t)\) over \(k\) such that \(f(t)=F(p(t))\) and \(g(t)=F(q(t)).\) The ...
David R. Barton, Richard Zippel
openaire +1 more source
Shortening the order of paraunitary matrices in SBR2 algorithm [PDF]
, 2007 The second order sequential best rotation (SBR2) algorithm has recently been proposed as a very effective tool in decomposing a para-Hermitian polynomial matrix R(z) into a diagonal polynomial matrix T(z) and a paraunitary matrix B(,z), extending the ...
Weiss, Stephan +5 more
core +1 more source
Journal of Mathematical Cryptology, 2022 We investigate the problem of recovering integer inputs (up to an affine scaling) when given only the integer monotonic polynomial outputs. Given nn integer outputs of a degree-dd integer monotonic polynomial whose coefficients and inputs are integers ...
Vivek Srinivas +2 more
doaj +1 more source
Division algorithms for Bernstein polynomials [PDF]
Computer Aided Geometric Design, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Busé, Laurent, Goldman, Ron
openaire +1 more source
A two-variable approach to solve the polynomial Lyapunov equation [PDF]
, 2001 A two-variable polynomial approach to solve the one-variable polynomial Lyapunov equation is proposed. Lifting the problem from the one-variable to the two-variable context allows to use Faddeev-type recursions in order to solve the polynomial Lyapunov ...
Peeters, Ralf +4 more
core +1 more source
IET Control Theory & Applications, 2021 A polynomial filtering algorithm is designed for estimating a Markov sequence based on linear measurements. The feature of the estimation problem is that the Markov sequence is described by a nonlinear shaping filter, which is a second‐order polynomial ...
O. A. Stepanov +4 more
doaj +1 more source
Limitations of the Macaulay matrix approach for using the HHL algorithm to solve multivariate polynomial systems [PDF]
Quantum, 2023 Recently Chen and Gao \cite{ChenGao2017} proposed a new quantum algorithm for Boolean polynomial system solving, motivated by the cryptanalysis of some post-quantum cryptosystems.
Jintai Ding +4 more
doaj +1 more source
Polynomial decomposition algorithms
Journal of Symbolic Computation, 1989 A polynomial \(f\) over a commutative ring is said to be decomposable if it has a non-trivial functional decomposition \(f=g\circ h\). Previous algorithms to check decomposability were exponential-time in the worst case and only worked over fields of characteristic 0.
Dexter Kozen, Susan Landau 0001
openaire +2 more sources
Algorithmic Computation of Polynomial Amoebas [PDF]
, 2016 We present algorithms for computation and visualization of amoebas, their contours, compactified amoebas and sections of three-dimensional amoebas by two-dimensional planes. We also provide method and an algorithm for the computation of~polynomials whose amoebas exhibit the most complicated topology among all polynomials with a fixed Newton polytope ...
D. V. Bogdanov +2 more
openaire +5 more sources
Broadband angle of arrival estimation methods in a polynomial matrix decomposition framework [PDF]
, 2013 A large family of broadband angle of arrival estimation algorithms are based on the coherent signal subspace (CSS) method, whereby focussing matrices appropriately align covariance matrices across narrowband frequency bins.
Mohamed Alrmah +9 more
core +1 more source