6 citations · 37 across the 17 of their papers we have counts for
17 papers
Fast Approximation of Polynomial Zeros and Matrix Eigenvalues
Victor Y. Pan, Soo Go, Qi Luan +1
We approximate the d complex zeros of a univariate polynomial p(x) of a degree d or those zeros that lie in a fixed region of interest on the complex plane such as a disc or a squa…
CUR Low Rank Approximation at Deterministic Sublinear Cost
Qi Luan, Victor Y. Pan, John Svadlenka
A matrix algorithm runs at {\em sublinear cost} if it uses much fewer memory cells and arithmetic operations than the input matrix has entries. Such algorithms are indispensable fo…
Counting Roots of a Polynomial in a Convex Compact Region by Means of Winding Number Calculation via Sampling
Vitaly Zaderman, Liang Zhao
In this paper we propose a novel efficient algorithm for calculating winding numbers, aiming at counting the number of roots of a given polynomial in a convex region on the complex…
Low Rank Approximation at Sublinear Cost
Qi Luan, Victor Y. Pan, John Svadlenka +1
Low Rank Approximation (LRA) of a matrix is a hot research subject, fundamental for Matrix and Tensor Computations and Big Data Mining and Analysis. Computations with low rank matr…
CUR Low Rank Approximation of a Matrix at Sublinear Cost
Soo Go, Qi Luan, Victor Y. Pan +2
Low rank approximation of a matrix (hereafter LRA) is a highly important area of Numerical Linear and Multilinear Algebra and Data Mining and Analysis. One can operate with an LRA…
Convergence and Applications of ADMM on the Multi-convex Problems
Junxiang Wang, Liang Zhao
In recent years, although the Alternating Direction Method of Multipliers (ADMM) has been empirically applied widely to many multi-convex applications, delivering an impressive per…
Superfast Low Rank Approximation
Soo Go, Qi Luan, Victor Y. Pan +2
Low rank approximation of a matrix (LRA) is a highly important area of Numerical Linear and Multilinear Algebra and Data Mining and Analysis. One can operate with an LRA superfast…
Superfast CUR Matrix Algorithms, Their Pre-Processing and Extensions
Victor Y. Pan, Qi Luan, John Svadlenka +1
We study superfast algorithms that computes low rank approximation of a matrix (hereafter referred to as LRA) that use much fewer memory cells and arithmetic operations than the in…
Superfast Low-Rank Approximation and Least Squares Regression
Victor Y. Pan, Qi Luan, John Svadlenka +1
Low Rank Approximation is among most fundamental subjects of numerical linear algebra having important applications to various areas of modern computing and %they range from machin…
Fast Derandomized Low-rank Approximation and Extensions
Victor Pan, John Svadlenka, Liang Zhao
Low-rank approximation of a matrix by means of structured random sampling has been consistently efficient in its extensive empirical studies around the globe, but adequate formal s…
Highly Efficient Computation of Generalized Inverse of a Matrix
V. Y. Pan, F. Soleymani, Liang Zhao
We propose a hyperpower iteration for numerical computation of the outer generalized inverse of a matrix which achieves the 18th order of convergence by using only seven matrix mul…
Low-rank Approximation of a Matrix: Novel Insights, New Progress, and Extensions
Victor Y. Pan, Liang Zhao
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and st…
Accelerated Approximation of the Complex Roots and Factors of a Univariate Polynomial
Victor Y. Pan, Elias P. Tsigaridas, Vitaly Zaderman +1
The algorithms of Pan (1995) and(2002) approximate the roots of a complex univariate polynomial in nearly optimal arithmetic and Boolean time but require precision of computing tha…
Real Polynomial Root-finding by Means of Matrix and Polynomial Iterations
Victor Y. Pan, Liang Zhao
Univariate polynomial root-finding is a classical subject, still important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. Th…
Polynomial Root Isolation by Means of Root Radii Approximation
Victor Y. Pan, Liang Zhao
Univariate polynomial root-finding is a classical subject, still important for modern computing. Frequently one seeks just the real roots of a real coefficient polynomial. They can…
Numerically Safe Gaussian Elimination with No Pivoting
Victor Pan, Liang Zhao
Gaussian elimination with no pivoting and block Gaussian elimination are attractive alternatives to the customary but communication intensive Gaussian elimination with partial pivo…
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…