526 research outputs found
Global spectrum fluctuations for the -Hermite and -Laguerre ensembles via matrix models
We study the global spectrum fluctuations for -Hermite and
-Laguerre ensembles via the tridiagonal matrix models introduced in
\cite{dumitriu02}, and prove that the fluctuations describe a Gaussian process
on monomials. We extend our results to slightly larger classes of random
matrices.Comment: 43 pages, 2 figures; typos correcte
Accurate and Efficient Expression Evaluation and Linear Algebra
We survey and unify recent results on the existence of accurate algorithms
for evaluating multivariate polynomials, and more generally for accurate
numerical linear algebra with structured matrices. By "accurate" we mean that
the computed answer has relative error less than 1, i.e., has some correct
leading digits. We also address efficiency, by which we mean algorithms that
run in polynomial time in the size of the input. Our results will depend
strongly on the model of arithmetic: Most of our results will use the so-called
Traditional Model (TM). We give a set of necessary and sufficient conditions to
decide whether a high accuracy algorithm exists in the TM, and describe
progress toward a decision procedure that will take any problem and provide
either a high accuracy algorithm or a proof that none exists. When no accurate
algorithm exists in the TM, it is natural to extend the set of available
accurate operations by a library of additional operations, such as , dot
products, or indeed any enumerable set which could then be used to build
further accurate algorithms. We show how our accurate algorithms and decision
procedure for finding them extend to this case. Finally, we address other
models of arithmetic, and the relationship between (im)possibility in the TM
and (in)efficient algorithms operating on numbers represented as bit strings.Comment: 49 pages, 6 figures, 1 tabl
Distance-regular graphs
This is a survey of distance-regular graphs. We present an introduction to
distance-regular graphs for the reader who is unfamiliar with the subject, and
then give an overview of some developments in the area of distance-regular
graphs since the monograph 'BCN' [Brouwer, A.E., Cohen, A.M., Neumaier, A.,
Distance-Regular Graphs, Springer-Verlag, Berlin, 1989] was written.Comment: 156 page
Inverse M-matrices, II
AbstractThis is an update of the 1981 survey by the first author. In the meantime, a considerable amount has been learned about the very special structure of the important class of inverse M-matrices. Developments since the earlier survey are emphasized, but we have tried to be somewhat complete; and, some results have not previously been published. Some proofs are given where appropriate and references are given for others. After some elementary preliminaries, results are grouped by certain natural categories
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