Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan

1. Front Matter

   Pages i-xlix

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2. On Quasi-Energy-Spectra, Pair Correlations of Sequences and Additive Combinatorics

   • Ida Aichinger, Christoph Aistleitner, Gerhard Larcher

   Pages 1-16

3. Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains

   • Mark Ainsworth, Christian Glusa

   Pages 17-57

4. Irregularities of Distributions and Extremal Sets in Combinatorial Complexity Theory

   • Christoph Aistleitner, Aicke Hinrichs

   Pages 59-74

5. Importance Sampling and Stratification for Copula Models

   • Philipp Arbenz, Mathieu Cambou, Marius Hofert, Christiane Lemieux, Yoshihiro Taniguchi

   Pages 75-96

6. A Spectral Method for the Biharmonic Equation

   • Kendall Atkinson, David Chien, Olaf Hansen

   Pages 97-118

7. Quasi-Monte Carlo for an Integrand with a Singularity Along a Diagonal in the Square

   • Kinjal Basu, Art B. Owen

   Pages 119-130

8. There Is No Strongly Regular Graph with Parameters (460, 153, 32, 60)

   • Andriy Bondarenko, Anton Mellit, Andriy Prymak, Danylo Radchenko, Maryna Viazovska

   Pages 131-134

9. Low-Discrepancy Sequences for Piecewise Smooth Functions on the Torus

   • Luca Brandolini, Leonardo Colzani, Giacomo Gigante, Giancarlo Travaglini

   Pages 135-152

10. Explicit Families of Functions on the Sphere with Exactly Known Sobolev Space Smoothness

    • Johann S. Brauchart

    Pages 153-177

11. Logarithmic and Riesz Equilibrium for Multiple Sources on the Sphere: The Exceptional Case

    • Johann S. Brauchart, Peter D. Dragnev, Edward B. Saff, Robert S. Womersley

    Pages 179-203

12. Numerical Analysis and Computational Solution of Integro-Differential Equations

    • Hermann Brunner

    Pages 205-231

13. Multivariate Approximation in Downward Closed Polynomial Spaces

    • Albert Cohen, Giovanni Migliorati

    Pages 233-282

14. Subperiodic Trigonometric Hyperinterpolation

    • Gaspare Da Fies, Alvise Sommariva, Marco Vianello

    Pages 283-304

15. Discrete Data Fourier Deconvolution

    • Frank de Hoog, Russell Davies, Richard Loy, Robert Anderssen

    Pages 305-316

16. Kernels of a Class of Toeplitz Plus Hankel Operators with Piecewise Continuous Generating Functions

    • Victor D. Didenko, Bernd Silbermann

    Pages 317-337

17. Probabilistic Lower Bounds for the Discrepancy of Latin Hypercube Samples

    • Benjamin Doerr, Carola Doerr, Michael Gnewuch

    Pages 339-350

18. Hyperinterpolation for Spectral Wave Propagation Models in Three Dimensions

    • Mahadevan Ganesh, Stuart C. Hawkins

    Pages 351-372

19. Multilevel QMC with Product Weights for Affine-Parametric, Elliptic PDEs

    • Robert N. Gantner, Lukas Herrmann, Christoph Schwab

    Pages 373-405

20. An Adaptive Filon Algorithm for Highly Oscillatory Integrals

    • Jing Gao, Arieh Iserles

    Pages 407-424

This book is a tribute to Professor Ian Hugh Sloan on the occasion of his 80th birthday. It consists of nearly 60 articles written by international leaders in a diverse range of areas in contemporary computational mathematics. These papers highlight the impact and many achievements of Professor Sloan in his distinguished academic career. The book also presents state of the art knowledge in many computational fields such as quasi-Monte Carlo and Monte Carlo methods for multivariate integration, multi-level methods, finite element methods, uncertainty quantification, spherical designs and integration on the sphere, approximation and interpolation of multivariate functions, oscillatory integrals, and in general in information-based complexity and tractability,  as well as in a range of other topics.

The book also tells the life story of the renowned mathematician, family man, colleague and friend, who has been an inspiration to many of us. The reader may especially enjoy the story from the perspective of his family, his wife, his daughter and son, as well as grandchildren, who share their views of Ian. The clear message of the book is that Ian H. Sloan has been a role model in science and life.

• Electron-atom scattering
• Few-nucleon scattering problems
• Four-body problem, and the Bencze-Redish-Sloan equations
• Numerical integration and product integration
• Numerical analysis of second-kind integral equations
• Superconvergence of the iterated Galerkin approximation
• Boundary integral equations
• Qualocation
• Numerical analysis of partial differential equations
• Constructive approximation on spheres and manifolds
• Hyperinterpolation, radial basis functions, needlets
• High dimensional integration and approximation
• Weighted spaces of multivariate functions
• Information based complexity
• Tractability of multivariate and infinite-dimensional problems
• Numerical analysis of PDEs with random coefficients
• Applications in finance, groundwater flow, physics
• algorithmic complexity

• School of Mathematics and Statistics, University of New South Wales, Sydney, Australia

  Josef Dick, Frances Y. Kuo

• Department of Computer Science, Columbia University, New York, USA

  Henryk Woźniakowski

Josef Dick is Associate Professor in the School of Mathematics and Statistics at the University of New South Wales Sydney, Australia. He is a former PhD student of Professor Ian Sloan and currently Head of the Applied Mathematics Department in the School.

Frances Kuo is Associate Professor in the School of Mathematics and Statistics at the University of New South Wales Sydney, Australia. She is an academic grandchild of Professor Ian Sloan and a collaborator for over 15 years.

Henryk Wozniakowski is Emeritus Professor of Columbia University in New York and of University of Warsaw in Poland. He has been collaborating with Professor Ian Sloan for the last 20 years.

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