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

By Arieh Iserles

Acta Numerica surveys each year crucial advancements in numerical arithmetic and clinical computing. the themes and authors of the great survey articles are selected via a exceptional overseas editorial board in an effort to file crucial and well timed advancements in a fashion obtainable to the broader group of execs with an curiosity in clinical computing. Acta Numerica volumes have proved to be a invaluable device not just for researchers and execs wishing to boost their realizing of numerical strategies and algorithms and keep on with new advancements, but additionally as a complicated educating relief at faculties and universities. the various unique articles were used because the best source for graduate classes. this actual quantity was once initially released in 2004.

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Anal. Ser. B 2, 205-224. G. H. Golub and R. J. Plemmons (1980), 'Large-scale geodetic least-squares adjustment by dissection and orthogonal decomposition', Linear Algebra Appl. 34, 3-28. 27 on Tue Nov 09 11:59:45 GMT 2010. 001 Cambridge Books Online © Cambridge University Press, 2010 50 A. BJORCK G. H. Golub and C. Reinsch (1970), 'Singular value decomposition and least squares solution', Numer. Math. 14, 403-420. G. H. Golub and C. F. Van Loan (1996), Matrix Computations, 3rd edn, Johns Hopkins University Press, Baltimore.

The sensitivity of the solution of problem LSI to perturbations in the data A, B, b is also studied in Lotstedt (1983). An important special case of problem LSI is when the inequalities are simple bounds, problem BLS: min ||AE-6||2. 2). If rank(vl) = n the BLS problem is a strictly convex optimization problem and there exists a unique solution for any vector b. 27 on Tue Nov 09 11:59:42 GMT 2010. 001 Cambridge Books Online © Cambridge University Press, 2010 34 A. BJORCK Sometimes only one-sided bounds apply.

3. QR decomposition for general sparse matrices The factor R in the QR decomposition of A is mathematically equivalent to the Cholesky factor of the cross product matrix ATA. Although this is true in exact arithmetic the difficulty in recognizing numerical cancellation means that the computed structure of the Cholesky factor can overestimate the structure of R. However, in many cases it accurately predicts the structure of R. 27 on Tue Nov 09 11:59:44 GMT 2010. 001 Cambridge Books Online © Cambridge University Press, 2010 42 A.

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