14 citations · 89 across the 38 of their papers we have counts for
45 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…
New Progress in Classic Area: Polynomial Root-squaring and Root-finding
Victor Y. Pan
The DLG root-squaring iterations, due to Dandelin 1826 and rediscovered by Lobachevsky 1834 and Graeffe 1837, have been the main approach to root-finding for a univariate polynomia…
Accelerated Subdivision for Clustering Roots of Polynomials given by Evaluation Oracles
Rémi Imbach, Victor Y. Pan
In our quest for the design, the analysis and the implementation of a subdivision algorithm for finding the complex roots of univariate polynomials given by oracles for their evalu…
Root Radii and Subdivision for Polynomial Root-Finding
Rémi Imbach, Victor Y. Pan
We depart from our approximation of 2000 of all root radii of a polynomial, which has readily extended Sch{ö}nhage's efficient algorithm of 1982 for a single root radius. We revisi…
New practical advances in polynomial root clustering
Rémi Imbach, Victor Y. Pan
We report an ongoing work on clustering algorithms for complex roots of a univariate polynomial of degree with real or complex coefficients. As in their previous best subdi…
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…