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NUMERICAL ANALYSIS 2000: VOL 3 LINEAR ALGEBRA LINEAR SYSTEMS AND
P.M.van Dooren, A. Hadjidimos, H.A.vander Vorst
With the year 2000 being elected 'The World Mathematical Year', the Journal of Computational and Applied Mathematics decided to publish a series of volumes dedicated to various disciplines of applied mathematics and numerical analysis. The series received the ambitious title Numerical Analysis in the 20th Century' and contains seven volumes of which the present one is devoted to 'Linear Algebra'.
From the early days of scientific computing, numerical linear algebra has been driven by the necessity to be able to solve linear systems, to solve eigenproblems, and to understand the meaning of the results. Because many of these problems have to be solved repeatedly in other computational problems, the algorithms have to be robust and as fast as possible. This has led to much activity, and other than only developing algorithms on demand, the involved research has been equally intellectually challenging as in other sciences. The behavior of algorithms under rounding errors was a great source of inspiration for the further development of perturbation theory.
The papers in this volume can be roughly subdivided into the following groups:
1. Eigenproblems (including SVD). 2. Linear Systems. 3. Miscellaneous problems and 4. Software.
Foreword: Numerical Analysis 2000. Vol. III: Linear Algebra (A. Hadjidimos, H. van der Vorst, P. Van Dooren). Iterative solution of linear systems in the 20th century (Y. Saad, H.A. van der Vorst). Eigenvalue computation in the 20th century (G.H. Golub, H.A. van der Vorst). QR -like algorithms for eigenvalue problems (D.S. Watkins). The ubiquitous Kronecker product (C.F. Van Loan). Preconditioning eigenvalues and some comparison of solvers (R.B. Morgan). For tridiagonals T replace T with LDL t (B.N. Parlett). An overview of relative sin &THgr; theorems for invariant subspaces of complex matrices (I.C.F. Ipsen). The trace minimization method for the symmetric generalized eigenvalue problem (A. Sameh, Z. Tong). Successive overrelazation (SOR) and related methods (A. Hadjidimos). On asynchronous iterations (A. Frommer, D.B. Szyld). Iterative methods for large continuation problems (D. Calvetti, L. Reichel). The matrix and polynomial approaches to Lanczos-type algorithms (C. Brezinski, M. Redivo-Zaglia, H. Sadok). Analysis of acceleration strategies for restarted minimal residual methods (M. Eiermann, O.G. Ernst, O. Schneider). Refining an approximate inverse (R. Bridson, W.-P. Tang). Scalable preconditioned conjugate gradient inversion of vector finite element mass matrices (J. Koning, G. Rodrigue, D. White). Robust multigrid methods for nonsmooth coefficient elliptic linear systems (T.F. Chan, W.L. Wan). The Rook's pivoting strategy (G. Poole, L. Neal). Numerical methods in control (V. Mehrman, H. Xu). Krylov-subspace methods for reduced-order modeling in circuit simulation (R.W. Freund). Tikhonov regularization and the L-curve for large discrete ill-posed problems (D. Calvetti, S. Morigi, L. Reichel, F. Sgallari). Symbiosis between linear algebra and optimization (D.P. O'Leary). Some computational problems arising in adaptive optics imaging systems (R.J. Plemmons, V.P. Pauca). Numerical linear algebra algorithms and software (J.J. Dongarra, V. Eijkhout). The impact of high-performance computing in the solution of linear systems: trends and problems (I.S. Duff). Series: Numerical Analysis 2000