14 citations · 89 across the 38 of their papers we have counts for
5 papers · 2 filters
New Studies of Randomized Augmentation and Additive Preprocessing
Victor Y. Pan, Liang Zhao
1. A standard Gaussian random matrix has full rank with probability 1 and is well-conditioned with a probability quite close to 1 and converging to 1 fast as the matrix deviates fr…
Better Late Than Never: Filling a Void in the History of Fast Matrix Multiplication and Tensor Decompositions
Victor Y. Pan
Multilinear and tensor decompositions are a popular tool in linear and multilinear algebra and have a wide range of important applications to modern computing. Our paper of 1972 pr…
Random Multipliers Numerically Stabilize Gaussian and Block Gaussian Elimination: Proofs and an Extension to Low-rank Approximation
Victor Y. Pan, Guoliang Qian, Xiaodong Yan
We prove that standard Gaussian random multipliers are expected to numerically stabilize both Gaussian elimination with no pivoting and block Gaussian elimination. Moreover we prov…
Global Newton Iteration over Archimedean and non-Archimedean Fields
Jonathan D. Hauenstein, Victor Pan, Agnes Szanto
In this paper, we study iterative methods on the coefficients of the rational univariate representation (RUR) of a given algebraic set, called global Newton iteration. We compare t…
Novel Approach to Real Polynomial Root-finding and Matrix Eigen-solving
Victor Y. Pan
Univariate polynomial root-finding is both classical and important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can b…