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  1. No Access

    Article

    Analysis of an alignment algorithm for nonlinear dimensionality reduction

    The goal of dimensionality reduction or manifold learning for a given set of high-dimensional data points, is to find a low-dimensional parametrization for them. Usually it is easy to carry out this parametriz...

    Qiang Ye, Hongyuan Zha, Ren-Cang Li in BIT Numerical Mathematics (2007)

  2. No Access

    Article

    Modifying the generalized singular value decomposition with application with application in direction-of-arrival finding

    We consider updating and downdating problems for the generalized singular value decomposition (GSVD) of matrix pairs when new rows are added to one of the matrices or old rows are deleted. Two classes of algor...

    Hongyuan Zha, Zhenyue Zhang in BIT Numerical Mathematics (1998)

  3. No Access

    Article

    Computing the optimal commuting matrix pairs

    A matrix can be modified by an additive perturbation so that it commutes with any given matrix. In this paper, we discuss several algorithms for computing the smallest perturbation in the Frobenius norm for a ...

    Hongyuan Zha, Zhenyue Zhang in BIT Numerical Mathematics (1997)

  4. No Access

    Article

    An algorithm and a stability theory for downdating the ULV decomposition

    An alternative to performing the singular value decomposition is to factor a matrixA into $$A = U\left( {\begin{array}{*{20}c} C \\...

    Jesse L. Barlow, Peter A. Yoon, Hongyuan Zha in BIT Numerical Mathematics (1996)

  5. No Access

    Article

    Computing the generalized singular values/vectors of large sparse or structured matrix pairs

    We present a numerical algorithm for computing a few extreme generalized singular values and corresponding vectors of a sparse or structured matrix pair \(\{A,B\}\) . The algori...

    Hongyuan Zha in Numerische Mathematik (1996)

  6. No Access

    Article

    A note on constructing a symmetric matrix with specified diagonal entries and eigenvalues

    A finite step algorithm is given such that for any two vectorsa, λ ∈R n witha majorized by λ, it computes a symmetric matrixH ∈R n x n with ...

    Hongyuan Zha, Zhenyue Zhang in BIT Numerical Mathematics (1995)

  7. No Access

    Chapter and Conference Paper

    The Canonical Correlations of Matrix Pairs and their Numerical Computation

    This paper is concerned with the analysis of canonical correlations of matrix pairs and their numerical computation. We first develop a decomposition theorem for matrix pairs having the same number of rows whi...

    Gene H. Golub, Hongyuan Zha in Linear Algebra for Signal Processing (1995)

  8. No Access

    Article

    A look-ahead algorithm for the solution of general Hankel systems

    The solution of systems of linear equations with Hankel coefficient matrices can be computed with onlyO(n 2) arithmetic operations, as compared toO(n 3) operations for the general cases. However, the classical Ha...

    Roland W. Freund, Hongyuan Zha in Numerische Mathematik (1993)

  9. No Access

    Article

    The product-product singular value decomposition of matrix triplets

    A new decomposition of a matrix triplet (A, B, C) corresponding to the singular value decomposition of the matrix productABC is developed in this paper, which will be termed theProduct-Product Singular Value Deco...

    Hongyuan Zha in BIT Numerical Mathematics (1991)

  10. No Access

    Article

    ImplicitQR factorization of a product of three matrices

    We present a numerical algorithm for computing the implicit QR factorization of a product of three matrices, and we illustrate the technique by applying it to the generalized total least squares and the restri...

    Hongyuan Zha in BIT Numerical Mathematics (1991)