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

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By Arieh Iserles

Acta Numerica surveys every year an important advancements in numerical arithmetic and clinical computing. the themes and authors of the great survey articles are selected by way of a unusual overseas editorial board with the intention to file crucial and well timed advancements in a fashion obtainable to the broader neighborhood of pros with an curiosity in clinical computing. Acta Numerica volumes have proved to be a worthwhile device not just for researchers and pros wishing to boost their knowing of numerical concepts and algorithms and stick with new advancements, but in addition as a sophisticated educating relief at faculties and universities. a few of the unique articles were used because the leading source for graduate classes. this actual quantity was once initially released in 2004.

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001 Cambridge Books Online © Cambridge University Press, 2010 24 A. BJORCK that to is a unit vector such that \\Rw\\ — an. Let P and Q be orthogonal matrices such that QTw = en and PTRQ = R, where R is upper triangular. 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).

Cox and N. J. Higham (19996), 'Backward error bounds for constrained least squares problems', BIT 39, 210-227. M. G. Cox (1990), The least-squares solution of linear equations with block-angular observation matrix, in Reliable Numerical Computation (M. G. Cox and S. J. Hamrnarling, eds), Oxford University Press, UK, pp. 227-240. B. De Moor and P. Van Dooren (1992), 'Generalizations of the singular value and QR decompositions', SIAM J. Matrix. Anal. Appl. 13, 993-1014. B. De Moor and H. Zha (1991), 'A tree of generalizations of the ordinary singular value decomposition', Linear Algebra Appl.

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. Anal. Appl. 13, 333-356. J. R. Gilbert, E. G. Ng and B. W. Peyton (1997), 'Separators and structure prediction in sparse orthogonal factorization', Linear Algebra Appl. 262, 83-97. L. Giraud, J. Langou, and M. Rozlozmk (2002), On the loss of orthogonality in the Gram-Schmidt orthogonalization process, Technical report TR/PA/02/33, CERFACS, Toulouse, France.

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