## Mathematics of computation 1943-1993: A half-century of computational mathematics |

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### Contents

On the development of multigrid methods and their analysis | 5 |

An introduction to inverse problems | 21 |

A review of recent develop | 33 |

A survey of componentwise perturbation theory in numerical linear algebra | 49 |

Numerical evaluation of special functions | 79 |

A survey of numerical cubature over triangles | 127 |

New trends in the use and analysis of integral equations | 151 |

Applications of multivariate splines | 177 |

Orthogonal spline collocation solution of nonlinear Schrodinger equations | 355 |

Who invented the computer? The debate from the viewpoint of computer | 361 |

Locking and boundary layer effects in the finite element approximation | 367 |

Efficient spectral Galerkin methods for some elliptic problems | 373 |

Front tracking based on highresolution wave propagation methods | 383 |

Timesplitting methods for nonhomogeneous conservation laws | 389 |

Numerical aspects of uniform Airytype asymptotic expansions | 395 |

Computing integrals of the complex error function | 403 |

Development | 205 |

Multiresolution methods for partial differential equations | 225 |

A comparison of techniques for solving illconditioned problems arising | 243 |

A mixed spectralcollocation and operator splitting method for the Wigner | 249 |

Finite volume methods for irregular onedimensional grids | 255 |

Linear rational interpolation of continuous functions over an interval | 261 |

A new stabilizing constraint in illposed | 269 |

A finite element method for the 2D driftdiffusion semiconductor model | 275 |

Splitting functions and numerical analysis of WRtype methods for evolu | 281 |

Error estimates for a quadrature rule for Cauchy principal value integrals | 287 |

A numerical radius approach to stable difference schemes for parabolic | 293 |

The Faber polynomials for circular arcs | 301 |

Finite element approximation for optimal control of electrically conducting | 305 |

ADI methods for heat equations with discontinuities along an arbitrary | 311 |

Eigenvalue approximation of Fredholm integral operators | 317 |

Spectral methods for singular perturbation problems | 323 |

On constructing Chebyshev series solutions of differential equations | 333 |

Methods for solving large eigenvalue problems associated with configura | 343 |

Computing limiting normals to real surfaces | 349 |

Quadratures for improper integrals and their applications in integral equa | 409 |

Spline harmonic analysis and wavelet bases | 415 |

Minisymposium on Computational Number Theory | 421 |

Analytic computations in number theory | 451 |

The number field sieve | 465 |

Factoring integers before computers | 481 |

Explicit bounds for primes in residue classes | 535 |

Ramanujan and Eulers constant | 541 |

Congruential sieves on FPGA computers | 547 |

Lehmer pairs of zeros and the Riemann function | 553 |

Implications of computational mathematics for the philosophy of math | 561 |

Square roots of products of algebraic numbers | 567 |

A locally parameterized version of Lehmers problem | 573 |

Generalized Fermat numbers | 583 |

Evaluation of Ctf2 for some totally real algebraic number fields K | 589 |

The period of the Bell exponential integers modulo a prime | 595 |

603 | |

619 | |

### Common terms and phrases

1991 Mathematics Subject 1994 American Mathematical ACM Trans algebraic algorithm American Mathematical Society amicable pairs Anal analysis Appl applications approximation Bessel functions bound boundary box splines Chebyshev coefficients Comp complex componentwise Comput constant convergence cubature D. H. Lehmer decomposition defined denote differential equations discrete E-mail address eigenvalue elliptic estimates example expansion factorization field sieve finite element finite element method Fortran given grid integral equations interpolation inverse problem iteration Kraitchik Lenstra Lucas Math Mathematics Subject Classification matrix minimal multigrid methods nonlinear norm number field sieve number theory obtained operator optimal paper perturbation Phys polynomial primality testing prime numbers proof publication elsewhere quadratic residues quadratic sieve quadrature reduced ideal Riemann satisfies SIAM singular SLATEC smooth Software solution solving space splines square surface symmetric techniques Theorem triangle value problems variables vector Volume 48 wavelet zeros zeta function