TR-2011003: Partial Fraction Decomposition, Sylvester Matrices, Convolution and Newton's Iteration
نویسنده
چکیده
Both Sylvester matrix and convolution are defined by two polynomials. If one of them has small degree, then the associated Sylvester linear system can be solved fast by using its PFD interpretation of the convolution equation. This can immediately simplify the refinement of approximate convolution by means of Newton’s iteration, where we also incorporate the PFD refinement techniques or alternatively least-squares solution of a linear system associated with the convolution. The process is naturally extended to polynomial factorization and root-finding.
منابع مشابه
TR-2011004: Acceleration of Newton's Polynomial Factorization: Army of Constraints, Convolution, Sylvester Matrices, and Partial Fraction Decomposition
We try to arm Newton’s iteration for univariate polynomial factorization with greater convergence power by shifting to a larger basic system of multivariate constraints. The convolution equation is a natural means for a desired expansion of the basis for this iteration versus the classical univariate method, which is more vulnerable to foreign distractions from its convergence course. Compared ...
متن کاملAcceleration of Newton’s Polynomial Factorization: Army of Constraints, Convolution, Sylvester Matrices, and Partial Fraction Decomposition
We try to arm Newton’s iteration for univariate polynomial factorization with greater convergence power by shifting to a larger basic system of multivariate constraints. The convolution equation is a natural means for a desired expansion of the basis for this iteration versus the classical univariate method, which is more vulnerable to foreign distractions from its convergence course. Compared ...
متن کاملPartial Fraction Decomposition , Sylvester Matrices , Convolution and Newton ’ s Iteration ∗
Both Sylvester matrix and convolution are defined by two polynomials. If one of them has small degree, then the associated Sylvester linear system can be solved fast by using its PFD interpretation of the convolution equation. This can immediately simplify the refinement of approximate convolution by means of Newton’s iteration, where we also incorporate the PFD refinement techniques or alterna...
متن کاملAdaptive Eigenvalue Computations Using Newton's Method on the Grassmann Manifold
We consider the problem of updating an invariant subspace of a Hermitian, large and struc-tured matrix when the matrix is modiied slightly. The problem can be formulated as that of computing stationary values of a certain function, with orthogonality constraints. The constraint is formulated as the requirement that the solution must be on the Grassmann manifold, and Newton's method on the manif...
متن کاملA Class of Nested Iteration Schemes for Generalized Coupled Sylvester Matrix Equation
Global Krylov subspace methods are the most efficient and robust methods to solve generalized coupled Sylvester matrix equation. In this paper, we propose the nested splitting conjugate gradient process for solving this equation. This method has inner and outer iterations, which employs the generalized conjugate gradient method as an inner iteration to approximate each outer iterate, while each...
متن کامل