From: Stephen Vavasis Subject: Re: Parzial and total pivoting Date: Wed, 11 Oct 2000 11:04:49 -0400 Newsgroups: sci.math.num-analysis Summary: [missing] Alexander Tsyplakov wrote: > > Could you, please, cite just one example. I do not have > access to any of the books. > > ----------------------------- > Alexander Tsyplakov > Novosibirsk State University > http://www.nsu.ru/ef/tsy/ Wilkinson's original example is the matrix 1 0 0 0 -1 1 1 0 0 -1 1 1 1 0 -1 1 1 1 1 -1 1 1 1 1 -1 (and its generalization to higher dimensions). It's fairly clear that if you perform G.E. with partial pivoting on this matrix, and you assume that ties are broken to favor the entry on the diagonal, then the largest entry in the upper triangular factor is 2^(n-1). Growth like this could lead to a very inaccurate answer. Foster and Wright came up with examples of matrices of this kind that could come in practice (maybe). I think their examples were based on control theory. -- Steve Vavasis P.S. to Eric Rudd: I agree with everything in your last message. ============================================================================== From: Stephen Vavasis Subject: Re: Parzial and total pivoting Date: Wed, 11 Oct 2000 14:58:54 -0400 Newsgroups: sci.math.num-analysis Sorry, I made a mistake. The Wilkinson example is 1 0 0 0 1 -1 1 0 0 1 -1 -1 1 0 1 -1 -1 -1 1 1 -1 -1 -1 -1 1 See if that works any better than my previous example! -- Steve Vavasis Alexander Tsyplakov wrote: > > Sorry, Stephen, I'm missing the point. > > First, the matrix is clearly singular. Have you made a typo? > > Second, I do not see why largest entry in the upper > triangular factor is 2^(n-1). I've made a LDU decomposition, > choosing diagonal major elements and obtained the following: > > L = > 1. 0. 0. 0. 0. > 1. 1. 0. 0. 0. > 1. 1. 1. 0. 0. > 1. 1. 1. 1. 0. > 1. 1. 1. 1. 1. > > D = diag(1,1,1,1,0) > > U = > 1. 0. 0. 0. -1. > 0. 1. 0. 0. 0. > 0. 0. 1. 0. 0. > 0. 0. 0. 1. 0. > 0. 0. 0. 0. 1. > > ----------------------------- > Alexander Tsyplakov > Novosibirsk State University > http://www.nsu.ru/ef/tsy/ > > Stephen Vavasis wrote in message [quoted quote of previous message deleted --djr]