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Hardcover ISBN:  9780821802915 
Product Code:  PSAPM/48 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9780821892633 
Product Code:  PSAPM/48.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9780821802915 
eBook ISBN:  9780821892633 
Product Code:  PSAPM/48.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsProceedings of Symposia in Applied MathematicsVolume: 48; 1995; 644 ppMSC: Primary 65; 11
This volume, containing the proceedings of an international conference commemorating the fiftieth anniversary of Mathematics of Computation, reflects the unique way in which this journal views computational mathematics as including not only numerical analysis but also computational number theory. Accordingly, the book has two parts, one for each of these two branches. The major purpose of the conference was to take stock of the current state of the field, to reflect on its recent history, and to assess future trends. This is done in substantial survey papers written by recognized experts; there are ten such surveys in the first part and four in the second. The former cover such topics as multigrid and multiresolution methods, numerical linear algebra, methods for solving differential equations, splines and their applications, optimization, and approximation methods and software for special functions. The survey papers in the second part deal with the precomputer history of integer factorization and primality testing, as well as with some of the modern techniques of factorization and with computational techniques in analytic number theory and deterministic algorithms and their complexity in algebraic number theory. A glimpse into the very active contemporary scene is provided by the fortysix short contributed papers. With extensive bibliographic references, a detailed index, and language accessible to a wide audience, this book is an authoritative resource in the field of computational mathematics.
ReadershipNumerical analysts in academia and industry, engineers, physicists, mathematical historians, computational number theorists, and cryptographers.

Table of Contents

Part I. Symposium on numerical analysis

Invited papers

James H. Bramble — On the development of multigrid methods and their analysis [ MR 1314840 ]

Margaret Cheney — An introduction to inverse problems [ MR 1314841 ]

Donald Goldfarb — Algorithms for unconstrained optimization: a review of recent developments [ MR 1314842 ]

Nicholas J. Higham — A survey of componentwise perturbation theory in numerical linear algebra [ MR 1314843 ]

D. W. Lozier and F. W. J. Olver — Numerical evaluation of special functions [ MR 1314844 ]

J. N. Lyness and Ronald Cools — A survey of numerical cubature over triangles [ MR 1314845 ]

J.C. Nédélec — New trends in the use and analysis of integral equations [ MR 1314846 ]

Larry L. Schumaker — Applications of multivariate splines [ MR 1314847 ]

Hans J. Stetter — Initial value problems for ordinary differential equations: development of ideas, techniques, and implementation [ MR 1314848 ]

Roger Temam — Multiresolution methods for partial differential equations [ MR 1314849 ]

Contributed papers

Loyce Adams and Zhiyun Yang — A comparison of techniques for solving illconditioned problems arising from the immersed boundary method [ MR 1314850 ]

Anton Arnold — A mixed spectralcollocation and operator splitting method for the WignerPoisson equation

M. J. Berger, R. J. LeVeque and L. G. Stern — Finite volume methods for irregular onedimensional grids [ MR 1314852 ]

JeanPaul Berrut — Linear rational interpolation of continuous functions over an interval [ MR 1314853 ]

M. Brio and J. K. Hunter — A von Neumann reflection for the $2$D Burgers equation [ MR 1314854 ]

Alfred S. Carasso — Slow evolution from the boundary: A new stabilizing constraint on illposed continuation problems

Zhangxin Chen — A finite element method for the 2D driftdiffusion semiconductor model [ MR 1314856 ]

S. De Marchi, M. Vianello and R. Zanovello — Splitting functions and numerical analysis of WRtype methods for evolutionary and stationary problems [ MR 1314857 ]

Kai Diethelm — Error estimates for a quadrature rule for Cauchy principal value integrals [ MR 1314858 ]

Moshe Goldberg — A numerical radius approach to stable difference schemes for parabolic systems [ MR 1314859 ]

Takemitsu Hasegawa and Tatsuo Torii — An extension of the OlverSookne method for the solution of secondorder linear difference equations [ MR 1314860 ]

Matthew He — The Faber polynomials for circular arcs [ MR 1314861 ]

L. S. Hou and S. S. Ravindran — Finite element approximation for optimal control of electrically conducting fluid flows [ MR 1314862 ]

Zhi Lin Li and Anita Mayo — ADI methods for heat equations with discontinuities along an arbitrary interface [ MR 1314863 ]

E. B. Lin — Eigenvalue approximation of Fredholm integral operators [ MR 1314864 ]

Wen Bin Liu and T. Tang — Spectral methods for singular perturbation problems [ MR 1314865 ]

Niloufer Mackey — A quaternionJacobi method for symmetric matrices [ MR 1314866 ]

Allan J. MacLeod — On constructing Chebyshev series solutions of differential equations [ MR 1314867 ]

Athena Makroglou — Multiquadric collocation methods in the numerical solution of Volterra integral and integrodifferential equations [ MR 1314868 ]

Kristyn J. Maschhoff — Methods for solving large eigenvalue problems associated with configuration interaction electronic structure calculations

Donal O’Shea and Les Wilson — Computing limiting normals to real surfaces [ MR 1314869 ]

Mark P. Robinson — Orthogonal spline collocation solution of nonlinear Schrödinger equations [ MR 1314870 ]

Raúl Rojas — Who invented the computer? The debate from the viewpoint of computer architecture [ MR 1314871 ]

Christoph Schwab and Manil Suri — Locking and boundary layer effects in the finite element approximation of the ReissnerMindlin plate model [ MR 1314872 ]

Jie Shen — Efficient spectral Galerkin methods for some elliptic problems [ MR 1314873 ]

Qin Sheng and Ravi P. Agarwal — Periodic solutions of higherorder difference equations in two independent variables [ MR 1314874 ]

Keh Ming Shyue — Front tracking based on highresolution wave propagation methods [ MR 1314875 ]

T. Tang and Zhen Huan Teng — Timesplitting methods for nonhomogeneous conservation laws [ MR 1314876 ]

N. M. Temme — Numerical aspects of uniform Airytype asymptotic expansions [ MR 1314877 ]

Xin Wang, Edward K. Blum and Qingnan Li — Local dynamics and bifurcation consistencies of continuoustime dynamical systems and their numerical discretizations [ MR 1314878 ]

J. A. C. Weideman — Computing integrals of the complex error function [ MR 1314879 ]

Yuesheng Xu and Yunhe Zhao — Quadratures for improper integrals and their applications in integral equations [ MR 1314880 ]

Valery A. Zheludev — Spline harmonic analysis and wavelet bases [ MR 1314881 ]

Minisymposium on computational number theory dedicated to the memory of Derrick Henry Lehmer

Invited papers

Ingrid Biehl and Johannes Buchmann — Algorithms for quadratic orders [ MR 1314882 ]

Andrew M. Odlyzko — Analytic computations in number theory [ MR 1314883 ]

Carl Pomerance — The number field sieve [ MR 1314884 ]

H. C. Williams and J. O. Shallit — Factoring integers before computers [ MR 1314885 ]

Contributed papers

Eric Bach and Jonathan Sorenson — Explicit bounds for primes in residue classes [ MR 1314886 ]

Richard P. Brent — Ramanujan and Euler’s constant [ MR 1314887 ]

Nathan D. Bronson and Duncan A. Buell — Congruential sieves on FPGA computers [ MR 1314888 ]

George Csordas, Wayne Smith and Richard S. Varga — Lehmer pairs of zeros and the Riemann $\xi $function [ MR 1314889 ]

Andrew W. P. Guy and Richard K. Guy — A record aliquot sequence [ MR 1314890 ]

Andrew J. Lazarus — Implications of computational mathematics for the philosophy of mathematics [ MR 1314891 ]

Peter L. Montgomery — Square roots of products of algebraic numbers [ MR 1314892 ]

Gary A. Ray — A locally parameterized version of Lehmer’s problem [ MR 1314893 ]

H. J. J. te Riele — A new method for finding amicable pairs [ MR 1314894 ]

Hans Riesel and Anders Björn — Generalized Fermat numbers [ MR 1314895 ]

Kisao Takeuchi — Evaluation of $\zeta _K(2)$ for some totally real algebraic number fields $K$ of degree $9$ [ MR 1314896 ]

Samuel S. Wagstaff, Jr. — The period of the Bell exponential integers modulo a prime [ MR 1314897 ]

Changsheng Xu — Computing invariant polynomials of $p$adic reflection groups [ MR 1314898 ]


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This volume, containing the proceedings of an international conference commemorating the fiftieth anniversary of Mathematics of Computation, reflects the unique way in which this journal views computational mathematics as including not only numerical analysis but also computational number theory. Accordingly, the book has two parts, one for each of these two branches. The major purpose of the conference was to take stock of the current state of the field, to reflect on its recent history, and to assess future trends. This is done in substantial survey papers written by recognized experts; there are ten such surveys in the first part and four in the second. The former cover such topics as multigrid and multiresolution methods, numerical linear algebra, methods for solving differential equations, splines and their applications, optimization, and approximation methods and software for special functions. The survey papers in the second part deal with the precomputer history of integer factorization and primality testing, as well as with some of the modern techniques of factorization and with computational techniques in analytic number theory and deterministic algorithms and their complexity in algebraic number theory. A glimpse into the very active contemporary scene is provided by the fortysix short contributed papers. With extensive bibliographic references, a detailed index, and language accessible to a wide audience, this book is an authoritative resource in the field of computational mathematics.
Numerical analysts in academia and industry, engineers, physicists, mathematical historians, computational number theorists, and cryptographers.

Part I. Symposium on numerical analysis

Invited papers

James H. Bramble — On the development of multigrid methods and their analysis [ MR 1314840 ]

Margaret Cheney — An introduction to inverse problems [ MR 1314841 ]

Donald Goldfarb — Algorithms for unconstrained optimization: a review of recent developments [ MR 1314842 ]

Nicholas J. Higham — A survey of componentwise perturbation theory in numerical linear algebra [ MR 1314843 ]

D. W. Lozier and F. W. J. Olver — Numerical evaluation of special functions [ MR 1314844 ]

J. N. Lyness and Ronald Cools — A survey of numerical cubature over triangles [ MR 1314845 ]

J.C. Nédélec — New trends in the use and analysis of integral equations [ MR 1314846 ]

Larry L. Schumaker — Applications of multivariate splines [ MR 1314847 ]

Hans J. Stetter — Initial value problems for ordinary differential equations: development of ideas, techniques, and implementation [ MR 1314848 ]

Roger Temam — Multiresolution methods for partial differential equations [ MR 1314849 ]

Contributed papers

Loyce Adams and Zhiyun Yang — A comparison of techniques for solving illconditioned problems arising from the immersed boundary method [ MR 1314850 ]

Anton Arnold — A mixed spectralcollocation and operator splitting method for the WignerPoisson equation

M. J. Berger, R. J. LeVeque and L. G. Stern — Finite volume methods for irregular onedimensional grids [ MR 1314852 ]

JeanPaul Berrut — Linear rational interpolation of continuous functions over an interval [ MR 1314853 ]

M. Brio and J. K. Hunter — A von Neumann reflection for the $2$D Burgers equation [ MR 1314854 ]

Alfred S. Carasso — Slow evolution from the boundary: A new stabilizing constraint on illposed continuation problems

Zhangxin Chen — A finite element method for the 2D driftdiffusion semiconductor model [ MR 1314856 ]

S. De Marchi, M. Vianello and R. Zanovello — Splitting functions and numerical analysis of WRtype methods for evolutionary and stationary problems [ MR 1314857 ]

Kai Diethelm — Error estimates for a quadrature rule for Cauchy principal value integrals [ MR 1314858 ]

Moshe Goldberg — A numerical radius approach to stable difference schemes for parabolic systems [ MR 1314859 ]

Takemitsu Hasegawa and Tatsuo Torii — An extension of the OlverSookne method for the solution of secondorder linear difference equations [ MR 1314860 ]

Matthew He — The Faber polynomials for circular arcs [ MR 1314861 ]

L. S. Hou and S. S. Ravindran — Finite element approximation for optimal control of electrically conducting fluid flows [ MR 1314862 ]

Zhi Lin Li and Anita Mayo — ADI methods for heat equations with discontinuities along an arbitrary interface [ MR 1314863 ]

E. B. Lin — Eigenvalue approximation of Fredholm integral operators [ MR 1314864 ]

Wen Bin Liu and T. Tang — Spectral methods for singular perturbation problems [ MR 1314865 ]

Niloufer Mackey — A quaternionJacobi method for symmetric matrices [ MR 1314866 ]

Allan J. MacLeod — On constructing Chebyshev series solutions of differential equations [ MR 1314867 ]

Athena Makroglou — Multiquadric collocation methods in the numerical solution of Volterra integral and integrodifferential equations [ MR 1314868 ]

Kristyn J. Maschhoff — Methods for solving large eigenvalue problems associated with configuration interaction electronic structure calculations

Donal O’Shea and Les Wilson — Computing limiting normals to real surfaces [ MR 1314869 ]

Mark P. Robinson — Orthogonal spline collocation solution of nonlinear Schrödinger equations [ MR 1314870 ]

Raúl Rojas — Who invented the computer? The debate from the viewpoint of computer architecture [ MR 1314871 ]

Christoph Schwab and Manil Suri — Locking and boundary layer effects in the finite element approximation of the ReissnerMindlin plate model [ MR 1314872 ]

Jie Shen — Efficient spectral Galerkin methods for some elliptic problems [ MR 1314873 ]

Qin Sheng and Ravi P. Agarwal — Periodic solutions of higherorder difference equations in two independent variables [ MR 1314874 ]

Keh Ming Shyue — Front tracking based on highresolution wave propagation methods [ MR 1314875 ]

T. Tang and Zhen Huan Teng — Timesplitting methods for nonhomogeneous conservation laws [ MR 1314876 ]

N. M. Temme — Numerical aspects of uniform Airytype asymptotic expansions [ MR 1314877 ]

Xin Wang, Edward K. Blum and Qingnan Li — Local dynamics and bifurcation consistencies of continuoustime dynamical systems and their numerical discretizations [ MR 1314878 ]

J. A. C. Weideman — Computing integrals of the complex error function [ MR 1314879 ]

Yuesheng Xu and Yunhe Zhao — Quadratures for improper integrals and their applications in integral equations [ MR 1314880 ]

Valery A. Zheludev — Spline harmonic analysis and wavelet bases [ MR 1314881 ]

Minisymposium on computational number theory dedicated to the memory of Derrick Henry Lehmer

Invited papers

Ingrid Biehl and Johannes Buchmann — Algorithms for quadratic orders [ MR 1314882 ]

Andrew M. Odlyzko — Analytic computations in number theory [ MR 1314883 ]

Carl Pomerance — The number field sieve [ MR 1314884 ]

H. C. Williams and J. O. Shallit — Factoring integers before computers [ MR 1314885 ]

Contributed papers

Eric Bach and Jonathan Sorenson — Explicit bounds for primes in residue classes [ MR 1314886 ]

Richard P. Brent — Ramanujan and Euler’s constant [ MR 1314887 ]

Nathan D. Bronson and Duncan A. Buell — Congruential sieves on FPGA computers [ MR 1314888 ]

George Csordas, Wayne Smith and Richard S. Varga — Lehmer pairs of zeros and the Riemann $\xi $function [ MR 1314889 ]

Andrew W. P. Guy and Richard K. Guy — A record aliquot sequence [ MR 1314890 ]

Andrew J. Lazarus — Implications of computational mathematics for the philosophy of mathematics [ MR 1314891 ]

Peter L. Montgomery — Square roots of products of algebraic numbers [ MR 1314892 ]

Gary A. Ray — A locally parameterized version of Lehmer’s problem [ MR 1314893 ]

H. J. J. te Riele — A new method for finding amicable pairs [ MR 1314894 ]

Hans Riesel and Anders Björn — Generalized Fermat numbers [ MR 1314895 ]

Kisao Takeuchi — Evaluation of $\zeta _K(2)$ for some totally real algebraic number fields $K$ of degree $9$ [ MR 1314896 ]

Samuel S. Wagstaff, Jr. — The period of the Bell exponential integers modulo a prime [ MR 1314897 ]

Changsheng Xu — Computing invariant polynomials of $p$adic reflection groups [ MR 1314898 ]

Recommended.
ITW Nieuws