14 citations · 89 across the 38 of their papers we have counts for
8 papers · 1 filter
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…
Matrix Multiplication, Trilinear Decompositions, APA Algorithms, and Summation
Victor Y. Pan
Matrix multiplication (hereafter we use the acronym MM) is among the most fundamental operations of modern computations. The efficiency of its performance depends on various factor…
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…
Accelerated Approximation of the Complex Roots of a Univariate Polynomial (Extended Abstract)
Victor Y. Pan, Elias Tsigaridas
Highly efficient and even nearly optimal algorithms have been developed for the classical problem of univariate polynomial root-finding (see, e.g., \cite{P95}, \cite{P02}, \cite{MN…
Nearly Optimal Computations with Structured Matrices
Victor Y. Pan, Elias Tsigaridas
We estimate the Boolean complexity of multiplication of structured matrices by a vector and the solution of nonsingular linear systems of equations with these matrices. We study fo…