11 citations · 29 across the 6 of their papers we have counts for
6 papers
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…
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…
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…
More on the Power of Randomized Matrix Computations
Victor Y. Pan, Guoliang Qian
A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. Thi…
Condition Numbers of Random Toeplitz and Circulant Matrices
Victor Y. Pan, Guoliang Qian
Estimating the condition numbers of random structured matrices is a well known challenge, linked to the design of efficient randomized matrix algorithms. We deduce such estimates f…
Randomized Matrix Computations
Victor Y. Pan, Guoliang Qian, Ai-Long Zheng
Random matrices tend to be well conditioned, and we employ this well known property to advance matrix computations. We prove that our algorithms employing Gaussian random matrices…