Electronic ISBN:  9781470456375 
Product Code:  CONM/754.E 
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Book DetailsContemporary MathematicsVolume: 754; 2020; 364 ppMSC: Primary 11; 16; 35; 41; 65;
The year 2018 marked the 75th anniversary of the founding of Mathematics of Computation, one of the four primary research journals published by the American Mathematical Society and the oldest research journal devoted to computational mathematics. To celebrate this milestone, the symposium “Celebrating 75 Years of Mathematics of Computation” was held from November 1–3, 2018, at the Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island.
The sixteen papers in this volume, written by the symposium speakers and editors of the journal, include both survey articles and new contributions.
On the discrete side, there are four papers covering topics in computational number theory and computational algebra. On the continuous side, there are twelve papers covering topics in machine learning, high dimensional approximations, nonlocal and fractional elliptic problems, gradient flows, hyperbolic conservation laws, Maxwell's equations, Stokes's equations, a posteriori error estimation, and iterative methods. Together they provide a snapshot of significant achievements in the past quarter century in computational mathematics and also in important current trends.ReadershipGraduate students and research mathematicians interested in computational mathematics.

Table of Contents

Articles

Markus Bachmayr and Wolfgang Dahmen  Adaptive lowrank approximations for operator equations: Accuracy control and computational complexity

Fleurianne Bertrand and Daniele Boffi  The Prager–Synge theorem in reconstruction based a posteriori error estimation

Juan Pablo Borthagaray, Wenbo Li and Ricardo H. Nochetto  Linear and nonlinear fractional elliptic problems

Ronald Cools, Frances Y. Kuo, Dirk Nuyens and Ian H. Sloan  Lattice algorithms for multivariate approximation in periodic spaces with general weight parameters

Qiang Du, Bjorn Engquist and Xiaochuan Tian  Multiscale modeling, homogenization and nonlocal effects: Mathematical and computational issues

Michael Neilan  The Stokes complex: A review of exactly divergence–free finite element pairs for incompressible flows

Peter Monk and Yangwen Zhang  Finite element methods for Maxwell’s equations

Adam M. Oberman  Partial differential equation regularization for supervised machine learning

Yousef Saad  Iterative methods for linear systems of equations: A brief historical journey

Jie Shen and Xiaofeng Yang  The IEQ and SAV approaches and their extensions for a class of highly nonlinear gradient flow systems

ChiWang Shu  A class of boundpreserving high order schemes: The main ideas and recent developments

Olof B. Widlund  BDDC domain decomposition algorithms

Perlas Caranay, Matthew Greenberg and Renate Scheidler  Computing modular polynomials and isogenies of rank two Drinfeld modules over finite fields

Nicolas David and Paul Zimmermann  A new ranking function for polynomial selection in the number field sieve

Bettina Eick and Tobias Moede  A nilpotent quotient algorithm for finitely presented associative $\mathbb {Z}$algebras and its application to integral group rings

Michael J. Mossinghoff and Timothy S. Trudgian  A tale of two omegas


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The year 2018 marked the 75th anniversary of the founding of Mathematics of Computation, one of the four primary research journals published by the American Mathematical Society and the oldest research journal devoted to computational mathematics. To celebrate this milestone, the symposium “Celebrating 75 Years of Mathematics of Computation” was held from November 1–3, 2018, at the Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island.
The sixteen papers in this volume, written by the symposium speakers and editors of the journal, include both survey articles and new contributions.
On the discrete side, there are four papers covering topics in computational number theory and computational algebra. On the continuous side, there are twelve papers covering topics in machine learning, high dimensional approximations, nonlocal and fractional elliptic problems, gradient flows, hyperbolic conservation laws, Maxwell's equations, Stokes's equations, a posteriori error estimation, and iterative methods. Together they provide a snapshot of significant achievements in the past quarter century in computational mathematics and also in important current trends.
Graduate students and research mathematicians interested in computational mathematics.

Articles

Markus Bachmayr and Wolfgang Dahmen  Adaptive lowrank approximations for operator equations: Accuracy control and computational complexity

Fleurianne Bertrand and Daniele Boffi  The Prager–Synge theorem in reconstruction based a posteriori error estimation

Juan Pablo Borthagaray, Wenbo Li and Ricardo H. Nochetto  Linear and nonlinear fractional elliptic problems

Ronald Cools, Frances Y. Kuo, Dirk Nuyens and Ian H. Sloan  Lattice algorithms for multivariate approximation in periodic spaces with general weight parameters

Qiang Du, Bjorn Engquist and Xiaochuan Tian  Multiscale modeling, homogenization and nonlocal effects: Mathematical and computational issues

Michael Neilan  The Stokes complex: A review of exactly divergence–free finite element pairs for incompressible flows

Peter Monk and Yangwen Zhang  Finite element methods for Maxwell’s equations

Adam M. Oberman  Partial differential equation regularization for supervised machine learning

Yousef Saad  Iterative methods for linear systems of equations: A brief historical journey

Jie Shen and Xiaofeng Yang  The IEQ and SAV approaches and their extensions for a class of highly nonlinear gradient flow systems

ChiWang Shu  A class of boundpreserving high order schemes: The main ideas and recent developments

Olof B. Widlund  BDDC domain decomposition algorithms

Perlas Caranay, Matthew Greenberg and Renate Scheidler  Computing modular polynomials and isogenies of rank two Drinfeld modules over finite fields

Nicolas David and Paul Zimmermann  A new ranking function for polynomial selection in the number field sieve

Bettina Eick and Tobias Moede  A nilpotent quotient algorithm for finitely presented associative $\mathbb {Z}$algebras and its application to integral group rings

Michael J. Mossinghoff and Timothy S. Trudgian  A tale of two omegas