| Table of Contents |
| | List of Contributors | xi |
| pt. I | Commentaries | |
| 21. | Linear Recurrence Relations / Lisa Lorentzen | 3 |
| 22. | Ordinary Differential Equations / John Butcher | 7 |
| 23. | Computer Algorithms and Software Packages / Gradimir V. Milovanovic | 9 |
| | References | 10 |
| 24. | History and Biography / Gerhard Wanner | 11 |
| 24.1. | Euler | 11 |
| 24.2. | The Bieberbach Conjecture | 11 |
| 24.3. | Survey Articles | 12 |
| 24.4. | Biography | 12 |
| 25. | Miscellanea / Martin J. Gander | 13 |
| 25.1. | The FG Algorithm | 14 |
| 25.2. | Slowly Convergent Series | 15 |
| 25.3. | Slowly Convergent Series Occurring in Plate Contact Problems | 16 |
| 25.4. | The Hardy-Littlewood Function | 16 |
| 25.5. | The Spiral of Theodorus | 17 |
| 25.6. | Epilogue | 19 |
| | References | 19 |
| pt. II | Reprints | |
| 26. | Papers on Linear Recurrence Relations | 23 |
| 26.1. | [26] Computation of Successive Derivatives off(z)/z, Math. Comp. 20, 209--214 (1966) | 24 |
| 26.2. | [29] Computational Aspects of Three-Term Recurrence Relations, SIAM Rev. 9, 24--82 (1967) | 31 |
| 26.3. | [35] An Application of Minimal Solutions of Three-Term Recurrences to Coulomb Wave Functions, Aequationes Math. 2, 171--176 (1969) | 91 |
| 26.4. | [37] (with B. J. Klein) Recursive Computation of Certain Derivatives --- A Study of Error Propagation, Comm. ACM 13, 7--9 (1970) | 98 |
| 26.5. | [135] Is the Recurrence Relation for Orthogonal Polynomials Always Stable?, BIT 33, 277--284 (1993) | 102 |
| 26.6. | [150] The Computation of Special Functions by Linear Difference Equations, in Advances in difference equations (S. Elaydi, I. Gyori, and G. Ladas, eds.), 213--243 (1997) | 111 |
| 27. | Papers on Ordinary Differential Equations | 143 |
| 27.1. | [14] Numerical Integration of Ordinary Differential Equations Based on Trigonometric Polynomials, Numer. Math. 3, 381--397 (1961) | 144 |
| 27.2. | [54] Global Error Estimates in "One-Step" Methods for Ordinary Differential Equations, Rend. Mat. (2) 8, 601--617 (1975) (translated from Italian) | 162 |
| 27.3. | [73] (with M. Montrone) Multistep Methods With Minimum Global Error Coefficient, Calcolo 17, 67--75 (1980) (translated from Italian) | 178 |
| 28. | Papers on Computer Algorithms and Software Packages | 187 |
| 28.1. | [141] Algorithm 726: ORTHPOL --- A Package of Routines for Generating Orthogonal Polynomials and Gauss-type Quadrature Rules, ACM Trans. Math. Software 20, 21--62 (1994); Remark on Algorithm 726, ibid. 24, 355 (1998) | 188 |
| 28.2. | [179] Orthogonal Polynomials, Quadrature, and Approximation: Computational Methods and Software (in Matlab), in Orthogonal polynomials and special functions --- computation and applications (F. Marcellan and W. Van Assche, eds.), 1--77, Lecture Notes Math. 1883 (2006) | 231 |
| 29. | Papers on History and Biography | 309 |
| 29.1. | [74] A Survey of Gauss--Christoffel Quadrature Formulae, in E. B. Christoffel --- the influence of his work in mathematics and the physical sciences (P. L. Butzer and F. Feher, eds.), 72--147 (1981) | 311 |
| 29.2. | [91] (with J. Wimp) In Memoriam: Yudell L. Luke June 26, 1918 -- May 6, 1983, Math. Comp. 43, 349--352 (1984) | 388 |
| 29.3. | [101] Reminiscences of My Involvement in de Branges's Proof of the Bieberbach Conjecture, in The Bieberbach conjecture (A. Baernstein II, D. Drasin, P. Duren, and A. Marden, eds.), 205--211, Proc. Symp. on the Occasion of the Proof, Math. Surveys Monographs 21, American Mathematical Society (1986) | 393 |
| 29.4. | [143] The Work of Philip Rabinowitz on Numerical Integration, Numer. Algorithms 9, 199--222 (1995) | 401 |
| 29.5. | [144] Luigi Gatteschi's Work on Special Functions and Numerical Analysis, in Special functions (G. Allasia, ed.), Annals Numer. Math. 2, 3--19 (1995) | 426 |
| 29.6. | [170] The Interplay Between Classical Analysis and (Numerical) Linear Algebra --- A Tribute to Gene H. Golub, Electron. Trans. Numer. Anal. 13, 119--147 (2002) | 444 |
| 29.7. | [183] Leonhard Eulers Umgang mit langsam konvergenten Reihen, Elem. Math. 62, 174--183 (2007) | 474 |
| 29.8. | [184] Commentary, by Walter Gautschi, in Milestones in matrix computation: selected works of Gene H. Golub, with commentaries (R. H. Chan, Ch. Greif, and D. P. O'Leary, eds.), Ch. 22, 345--358, Oxford University Press (2007) | 485 |
| 29.9. | [186] On Euler's Attempt to Compute Logarithms by Interpolation: A Commentary to His Letter of February 16, 1734 to Daniel Bernoulli, J. Comput. Appl. Math. 219, 408--415 (2008) | 500 |
| 29.10. | [187] Leonhard Euler: His Life, the Man, and His Works, SIAM Rev. 50, 3--33 (2008). [Also published in ICIAM 07, 6th International Congress on Industrial and Applied Mathematics, Zurich, Switzerland, 16--20 July 2007 (R. Jeltsch and G. Wanner, eds.), 447--483, European Mathematical Society, (2009). Chinese translation in Mathematical Advance in Translation (2--3) [ect.] | 509 |
| 29.11. | [189] (with C. Giordano) Luigi Gatteschi's Work on Asymptotics of Special Functions and Their Zeros, in A collection of essays in memory of Luigi Gatteschi (G. Allasia, C. Brezinski, and M. Redivo-Zaglia, eds.), Numer. Algorithms 49, 11--31 (2008) | 541 |
| 29.12. | [196] Alexander M. Ostrowski (1893--1986): His Life, Work, and Students, in math.ch/100 Swiss Mathematical Society 1910--2010 (B. Colbois, C. Riedtmann, and V. Schroeder, eds.), 257--278, European Mathematical Society, (2010) | 563 |
| 29.13. | [201] My Collaboration with Gradimir V. Milovanovic, in Approximation and computation --- in honor of Gradimir V. Milovanovic (W. Gautschi, G. Mastroianni, and Th. M. Rassias, eds.), 33--43, Springer Optim. Appl. 42 (2011) | 586 |
| 30. | Papers on Miscellanea | 599 |
| 30.1. | [71] Families of Algebraic Test Equations, Calcolo 16, 383--398 (1979) | 600 |
| 30.2. | [96] (with B. N. Flury) An Algorithm for Simultaneous Orthogonal Transformation of Several Positive Definite Symmetric Matrices to Nearly Diagonal Form, SIAM J. Sci. Statist. Comput. 7, 169--184 (1986) | 617 |
| 30.3. | [124] A Class of Slowly Convergent Series and Their Summation by Gaussian Quadrature, Math. Comp. 57, 309--324 (1991) | 634 |
| 30.4. | [125] On Certain Slowly Convergent Series Occurring in Plate Contact Problems, Math. Comp. 57, 325--338 (1991) | 651 |
| 30.5. | [149] (with J. Waldvogel) Contour Plots of Analytic Functions, Ch. 25 in Solving problems in scientific computing using Maple and Matlab (W. Gander and J. Hfebicek, eds.), 3d ed., 359--372, Springer, Berlin, 1997. [Chinese translation by China Higher Education Press and Springer, 1999; Portuguese translation of 3d ed. by Editora Edgard Blucher Ltda., Sao Paulo, 2001; Russian translation of 4th ed. by Vassamedia, Minsk, Belarus, [ect.] | 666 |
| 30.6. | [175] The Hardy---Littlewood Function: An Exercise in Slowly Convergent Series, J. Comput. Appl. Math. 179, 249--254 (2005) | 681 |
| 30.7. | [197] The spiral of Theodorus, numerical analysis, and special functions, J. Comput. Appl. Math. 235, 1042--1052 (2010) | 688 |
| pt. III | Werner Gautschi | |
| 31. | Publications | 703 |
| | The Asymptotic Behaviour of Powers of Matrices, Duke Math. J. 20,127--140 (1953) | 704 |
| | The Asymptotic Behaviour of Powers of Matrices II, Duke Math. J. 20,375--379 (1953) | 719 |
| | Bounds of Matrices with Regard to an Hermitian Metric, Compositio Math. 12, 1--16 (1954) | 725 |
| | Some Remarks on Systematic Sampling, Ann. Math. Statist. 28, 385--394 (1957) | 742 |
| | Some Remarks on Herbach's Paper, Optimum Nature of the F-Test for Model II in the Balanced Case, Ann. Math. Statist. 30,960--963 (1959) | 753 |
| 32. | Obituaries | 759 |
| | "Werner Gautschi 1927--1959", Verh. Naturf. Ges. Basel 71, Nr. 2, 314--316 (1960) (English translation by Walter Gautschi) / A. Ostrowski | 760 |
| | "Werner Gautschi 1927--1959", Ann. Math. Statist. 31, 557 (1960) / J. R. Blum | 764 |
| 33. | Recording / Trout Quintet | 767 |
