Oct 12, 2003 · Title:Smoothed Analysis of the Condition Numbers and Growth Factors of Matrices. Authors:Arvind Sankar, Daniel A. Spielman, Shang-Hua Teng.

These matrices enable us to improve the known lower bounds on the largest possible growth factor in the case of complete pivoting. For partial pivoting, we ...

Dec 8, 2005 · In Section 5, we combine these results to obtain a smoothed bound on the precision needed by Gaussian elimination without pivoting. Definitions ...

It is shown that the smoothed precision necessary to solve Ax = b, for any b, using Gaussian elimination without pivoting is logarithmic.

We prove that it is unlikely that $A$ has large condition number. Using this result, we prove it is unlikely that $A$ has large growth factor under Gaussian ...

For numerous computation problems, the condition number of an input x of norm one, say, can be bounded up to a constant factor by the inverse distance of x to a ...

Abstract. We present some recent results on the probabilistic behaviour of interior point methods for the convex conic feasibility problem and for homotopy ...

Sankar, D.A. Spielman, S.H. Teng, Smoothed analysis of the condition numbers and growth factors of matrices, 2002, preprint. Google Scholar.

Obvious: Condition numbers are a crucial issue for designing. “numerically stable” algorithms. Less obvious, but true: Even when assuming infinite precision ...

Oct 22, 2024 · Smoothed Analysis of the Condition Numbers and Growth Factors of Matrices. Article. Nov 2003. Arvind Sankar · Daniel A. Spielman · Shang-Hua ...