Download Acta Numerica 2004: Volume 13 (Acta Numerica) by Arieh Iserles PDF

By Arieh Iserles

Acta Numerica surveys every year crucial advancements in numerical arithmetic and clinical computing. the themes and authors of the considerable survey articles are selected through a exotic overseas editorial board to be able to file crucial and well timed advancements in a way available to the broader group of execs with an curiosity in medical computing. Acta Numerica volumes have proved to be a necessary instrument not just for researchers and execs wishing to increase their knowing of numerical concepts and algorithms and keep on with new advancements, but in addition as a sophisticated instructing reduction at faculties and universities. the various unique articles were used because the major source for graduate classes. this actual quantity was once initially released in 2004.

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Duff (1997), Sparse numerical linear algebra: Direct methods and preconditioning, in The State of the Art in Numerical Analysis (I. S. Duff and G. A. Watson, eds), Oxford University Press, London, UK, pp. 27-62. L. Elden (1977), 'Algorithms for the regularization of ill-conditioned least squares problems', BIT 17, 134-145. L. Elden (1980), 'Perturbation theory for the least squares problem with linear equality constraints', SIAM J. Numer. Anal. 17, 338-350. 27 on Tue Nov 09 11:59:45 GMT 2010. 001 Cambridge Books Online © Cambridge University Press, 2010 THE CALCULATION OF LINEAR LEAST SQUARES PROBLEMS 49 L.

Then \\Ren\\ = \\PTRQQTw\\ = \\PTRw\\ = an, which shows that the entire last column in R is small. Given w the matrices P and Q can be constructed as a sequence of Givens rotations (see Stewart (1992), where algorithms are also given for updating a URV decomposition when a new row is appended). As for the RRQR decompositions, the URV decomposition yields approximations to the singular values. i, i= l : r , and where /= 1- - WRvWl Hence the smaller the norm of the off-diagonal block R\2, the better the bounds will be.

R. D. Fierro, P. Hansen, and P. S. K. Hansen (1999), 'UTV tools: Matlab templates for rank revealing UTV decompositions', Numer. Algorithms 20, 165-194. W. Gander (1981), 'Least squares with a quadratic constraint', Numer. Math. 36, 291-307. J. A. George and M. T. Heath (1980), 'Solution of sparse linear least squares problems using Givens rotations', Linear Algebra Appl. 34, 69-83. J. R. Gilbert, C. Moler and R. Schreiber (1992), 'Sparse matrices in MATLAB: Design and implementation', SIAM J. Matrix.

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