Xiaoying Wang
Functional CLT for sample covariance matrices.
Mon, 11/29/2010 - 16:01 — SomNambulAuthors: Wang Zhou, Xiaoying Wang, Zhidong Bai
Subjects: Statistics
AbstractUsing Bernstein polynomial approximations, we prove the central limit theorem
for linear spectral statistics of sample covariance matrices, indexed by a set
of functions with continuous fourth order derivatives on an open interval
including $[(1-\sqrt{y})^2,(1+\sqrt{y})^2]$, the support of the
Mar\u{c}enko--Pastur law. We also derive the explicit expressions for
asymptotic mean and covariance functions.Bivariate Lagrange Interpolation on Tower Interpolation Sites.
Mon, 01/11/2010 - 16:01 — SomNambulAuthors: Xiaoying Wang, Shugong Zhang, Tian Dong, Tao Chen
Subjects: Commutative Algebra
AbstractAs is well known, the geometry of the interpolation site of a multivariate
polynomial interpolation problem constitutes a dominant factor for the
structures of the interpolation polynomials. Solving interpolation problems on
interpolation sites with special geometries in theory may be a key step to the
development of general multivariate interpolation theory. In this paper, we
introduce a new type of 2-dimensional interpolation sites, tower interpolation
sites, whose associated degree reducing Lagrange interpolation monomial and
Newton bases w.r.t.A Bivariate Preprocessing Paradigm for Buchberger-M\"oller Algorithm.
Mon, 01/11/2010 - 16:01 — SomNambulAuthors: Xiaoying Wang, Shugong Zhang, Tian Dong
Subjects: Commutative Algebra
AbstractFor the last almost three decades, since the famous Buchberger-M\"oller(BM)
algorithm emerged, there has been wide interest in vanishing ideals of points
and associated interpolation polynomials. Our paradigm is based on the theory
of bivariate polynomial interpolation on cartesian point sets that gives us
related degree reducing interpolation monomial and Newton bases directly. Since
the bases are involved in the computation process as well as contained in the
final output of BM algorithm, our paradigm obviously simplifies the computation
and accelerates the BM process.
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