Results 1 to 10 of about 4,447 (309)
Polynomial J-spectral factorization [PDF]
IEEE Transactions on Automatic Control, 1994 The \(J\)-spectral factorization of para-Hermitian polynomial matrices \(Z(s)\) is considered. \(Z(s)\) is called para-Hermitian if \(Z^ \sim (s) : = Z^ T (-s) = Z(s)\). A spectral factorization of the form \(Z = P^ \sim JP\) with a signature matrix \(J\) is looked for.
Michael Šebek, H Kwakernaak
exaly +6 more sources
Practical polynomial factoring in polynomial time [PDF]
Proceedings of the 36th international symposium on Symbolic and algebraic computation, 2011 State of the art factoring in Q[x] is dominated in theory by a combinatorial reconstruction problem while, excluding some rare polynomials, performance tends to be dominated by Hensel lifting. We present an algorithm which gives a practical improvement (less Hensel lifting) for these more common polynomials.
William Hart +2 more
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Random polynomials and polynomial factorization [PDF]
, 1996 We give a precise average-case analysis of a complete polynomial factorization chain over finite fields by methods based on generating functions and singularity analysis.
Philippe Flajolet +2 more
core +6 more sources
Factorization of the Characteristic Polynomial [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We introduce a new method for showing that the roots of the characteristic polynomial of a finite lattice are all nonnegative integers. Our method gives two simple conditions under which the characteristic polynomial factors.
Joshua Hallam, Bruce Sagan
doaj +1 more source
Factorization of motion polynomials [PDF]
Journal of Symbolic Computation, 2019 In this paper, we consider the existence of a factorization of a monic, bounded motion polynomial. We prove existence of factorizations, possibly after multiplication with a real polynomial and provide algorithms for computing polynomial factor and factorizations.
Zijia Li +2 more
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The Numerical Factorization of Polynomials [PDF]
Foundations of Computational Mathematics, 2015 Polynomial factorization in conventional sense is an ill-posed problem due to its discontinuity with respect to coefficient perturbations, making it a challenge for numerical computation using empirical data. As a regularization, this paper formulates the notion of numerical factorization based on the geometry of polynomial spaces and the ...
Wenyuan Wu, Zhonggang Zeng
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Entanglement classification via operator size
SciPost Physics Core, 2023 In this work, multipartite entanglement is classified by polynomials. I show that the operator size is closely related to the entanglement structure. Given a generic quantum state, I define a series of subspaces generated by operators of different sizes ...
Qi-Feng Wu
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Factoring octonion polynomials [PDF]
International Journal of Algebra and Computation, 2020 We provide an analogue of Wedderburn’s factorization method for central polynomials with coefficients in an octonion division algebra, and present an algorithm for fully factoring polynomials of degree [Formula: see text] with [Formula: see text] conjugacy classes of roots, counting multiplicities.
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Trends in Computational and Applied Mathematics, 2023 The characterization of inverses of symmetric tridiagonal and block tridiagonal matrices and the development of algorithms for finding the inverse of any general non-singular tridiagonal matrix are subjects that have been studied by many authors.
C. G. Almeida, S. A. E. Remigio
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Factorization and Malleability of RSA Moduli, and Counting Points on Elliptic Curves Modulo N
Mathematics, 2020 In this paper we address two different problems related with the factorization of an RSA (Rivest–Shamir–Adleman cryptosystem) modulus N. First we show that factoring is equivalent, in deterministic polynomial time, to counting points on a pair of twisted
Luis V. Dieulefait, Jorge Urroz
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