14 citations · 89 across the 38 of their papers we have counts for
6 papers · 1 filter
Supporting GENP with Random Multipliers
Victor Y. Pan, Guoliang Qian, Xiaodong Yan
We prove that standard Gaussian random multipliers are expected to stabilize numerically both Gaussian elimination with no pivoting and block Gaussian elimination. Our tests show s…
New Structured Matrix Methods for Real and Complex Polynomial Root-finding
Victor Y. Pan, Ai-Long Zheng
We combine the known methods for univariate polynomial root-finding and for computations in the Frobenius matrix algebra with our novel techniques to advance numerical solution of…
Chapter 10: Algebraic Algorithms
Ioannis Z. Emiris, Victor Y. Pan, Elias P. Tsigaridas
Our Chapter in the upcoming Volume I: Computer Science and Software Engineering of Computing Handbook (Third edition), Allen Tucker, Teo Gonzales and Jorge L. Diaz-Herrera, editors…
Estimating the Norms of Random Circulant and Toeplitz Matrices and Their Inverses
Victor Y. Pan, Guolian Qian
We estimate the norms of standard Gaussian random Toeplitz and circulant matrices and their inverses, mostly by means of combining some basic techniques of linear algebra. In the c…
Transformations of Matrix Structures Work Again II
Victor Y. Pan
Matrices with the structures of Toeplitz, Hankel, Vandermonde and Cauchy types are omnipresent in modern computation. The four classes have distinct features, but in 1990 we showed…
Transformations of Matrix Structures Work Again
Victor Y. Pan
In 1989 we proposed to employ Vandermonde and Hankel multipliers to transform into each other the matrix structures of Toeplitz, Hankel, Vandermonde and Cauchy types as a means of…