Numerical Analysis : Historical Developments in the 20th Century

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Front Cover; Numerical Analysis: Historical Developments in the 20th Century; Copyright Page; Contents; Chapter 1. Numerical analysis in the twentieth century; The scenery; The actors; Landmarks; Acknowledgements:; References; Chapter 2. Approximation in normed linear spaces; Abstract; 1. Introduction; 2. Linear approximation; 3. Nonlinear approximation; Acknowledgements; References; Chapter 3. A tutorial history of least squares with applications to astronomy and geodesy; Abstract; 1. Introduction; 2. An ancient history of curve and surface fitting. 3. Weighted ordinary least squares and geodesy4. Unitary factorizations and constrained least squares; 5. The singular-value decomposition and error analysis; 6. Matrix approximation and total least squares; 7. Nonlinear least squares; References; Chapter 4. Convergence acceleration during the 20th century; 1. Introduction; 2. Scalar sequences; 3. The vector case; 4. Conclusions and perspectives; Acknowledgements; References; Chapter 5. On the history of multivariate polynomial interpolation; Abstract; 1. Introduction; 2. Kronecker, Jacobi and multivariate interpolation. 3. Bivariate tables, the natural approach4. Salzer's papers: from bivariate tables to general sets; 5. Reduction of a problem to other simpler ones; 6. The finite element approach; 7. Hermite problems; 8. Other approaches; Acknowledgements; References; Chapter 6. Numerical linear algebra algorithms and software; Abstract; 1. Introduction; 2. Dense linear algebra algorithms; 3. The influence of computer architecture on performance; 4. Dense linear algebra libraries; 5. Future research directions in dense algorithms; 6. Sparse linear algebra methods; 7. Direct solution methods. 8. Iterative solution methods9. Libraries and standards in sparse methods; References; Chapter 7. Iterative solution of linear systems in the 20th century; Abstract; 1. Introduction; 2. The quest for fast solvers: a historical perspective; 3. Relaxation-based methods; 4. Richardson and projection methods; 5. Second-order and polynomial acceleration; 6. Krylov subspace methods: the first period; 7. Krylov subspace methods: the second period; 8. Accelerators are not enough: preconditioning methods; 9. Multigrid methods; 10. Outlook; Acknowledgements; References. Chapter 8. Eigenvalue computation in the 20th centuryAbstract; 1. Sources; 2. Introduction; 3. Canonical forms; 4. Perturbation theorems; 5. Jacobi's method; 6. Power method; 7. Reduction algorithms; 8. Iterative methods; 9. Related topics; 10. Software; 11. Epilogue; Acknowledgements; References; Chapter 9. Historical developments in convergence analysis for Newton's and Newton-like methods; Abstract; 1. Introduction; 2. Newton's method; 3. Newton-like methods; 4. Secant method; 5. Halley's and Chebyshev's methods; 6. A class of iterative methods for not necessarily differentiable equations