8 Result(s)
within
Hongyuan Zha
Computational Mathematics and Numerical Analysis
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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...
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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...
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Chapter and Conference Paper
Large-scale SVD and subspace-based methods for information retrieval
A theoretical foundation for latent semantic indexing (LSI) is proposed by adapting a model first used in array signal processing to the context of information retrieval using the concept of subspaces. It is show...
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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 ...
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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 \\...
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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 ...
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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...
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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...
