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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On polynomial method and its application（II）
多项式方法 应用 代数
2023/5/17
We will introduce the polynomial partitioning method which has wide applications in incidence geometry, geometric measure theory, and harmonic analysis. In the first course, we will present some basic...
How to find all roots of complex polynomials by Newton’s method
complex polynomials Newton’s method
2015/8/26
We investigate Newton’s method to find roots of polynomials of fixed degree d, appropriately normalized: we construct a finite set of points such that, for every root of every such polynomial, at leas...
A bisection method for computing the H_infinity-norm of a transfer matrix and related problems
Transfer matrix singular value assessment the Hamiltonian matrix characteristic values of linear algebra
2015/8/13
Inspired by recent work of Byers we establish a simple connection between the singular values of a transfer matrix evaluated along the imaginary axis and the imaginary eigenvalues of a related Hamilto...
Method of centers for minimizing generalized eigenvalues
quasiconvex nondifferentiable optimization generalized eigenvalue linear fractional programming analytic center method of centers interior point method logarithmic barrier Newton algorithm path-following method ellipsoidal approximations
2015/8/12
We consider the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices, each of which depends affinely on the decision variables. Although this problem may appear spe...
A primal-dual operator splitting method for conic optimization
Character segmentation conic optimization yield distributed linear algebra
2015/8/7
We develop a simple operator splitting method for solving a primal conic optimization problem; we show that the iterates also solve the dual problem. The resulting algorithm is very simple to describe...
Rigid abelian groups and the probabilistic method
random construction abelian groups with prescribed endomorphisms probabilistic method Group Theory
2011/9/5
Abstract: The construction of torsion-free abelian groups with prescribed endomorphism rings starting with Corner's seminal work is a well-studied subject in the theory of abelian groups. Usually thes...
Stein's method and the multivariate CLT for traces of powers on the classical compact groups
random matrices compact Lie groups Haar measure traces of powers Stein’s method
2011/2/22
Let Mn be a random element of the unitary, special orthogonal, or unitary symplectic groups, distributed according to Haar measure. By a classical result of Diaconis and Shahshahani, for large matrix ...
An Inverse Power Method for Nonlinear Eigenproblems with Applications in 1-Spectral Clustering and Sparse PCA
Inverse Power Method for Nonlinear Eigenproblems Applications 1-Spectral Clustering Sparse PCA
2011/3/2
Many problems in machine learning and statistics can be formulated as (generalized)eigenproblems. In terms of the associated optimization problem, computing linear eigenvectors amounts to finding crit...
A finite volume method on general meshes for a degenerate parabolic convection-reaction-diffusion equation
parabolic convection-reaction-diffusion equation math
2010/11/23
We propose a finite volume method on general meshes for the discretization of a degenerate parabolic convection-reaction-diffusion equation. Equations of this type arise in many contexts, such as the ...
Lyapunov Computational Method for Two-Dimensional Boussinesq Equation
Lyapunov Computational Method Two-Dimensional Boussinesq Equation
2010/11/11
A numerical method is developed leading to Lyapunov operators to approximate the solution of two-dimensional Boussinesq equation. It consists of an order reduction method and a finite difference disc...
Lyapunov's method proves convergence to equilibrium for a thin film equation
Lyapunov's method proves convergence to equilibrium thin film equation
2010/11/15
The degenerate parabolic equation u_t + [u^3(u_xxx + u_x - sin x)]_x=0 with periodic boundary conditions models the evolution of a thin liquid film on a stationary horizontal cylinder. The equation d...
Dirac method and symplectic submanifolds in the cotangent bundle of a factorizable Lie group
Dirac method symplectic submanifolds cotangent bundle factorizable Lie group
2010/11/18
In this work we study some symplectic submanifolds in the cotangent bundle of a factorizable Lie group defined by second class constraints. By applying the Dirac method, we study many issues of these...
The Nyström method for functional quantization with an application to the fractional Brownian motion
integral equation Nyströ m method Gaussian semi-martingale functional quantization
2010/12/1
In this article, the so-called "Nyström method" is tested to compute optimal quantizers of Gaussian processes. In particular, we derive the optimal quantization of the fractional Brownian motion ...
A direct method for solving the generalized sine-Gordon equation
generalized sine-Gordon equation direct method
2010/4/1
The generalized sine-Gordon (sG) equation was derived as an integrable generalization of the sG equation. In this paper, we develop a direct method for solving the generalized sG equation without reco...
A Characteristic Set Method For Ordinary Di®erence Polynomial Systems
di® erence polynomial ascending chain characteristic set coherence irreducibility zero decomposition theorem automated theorem proving
2013/9/9
We prove several basic properties for di®erence ascending chains including a necessary and su±cient condition for an ascending chain to be the characteristic set of its saturation ideal and a nec...