Contents of Advances in Computational Mathematics

This file contains the tables of contents for all issues of Advances in Computational Mathematics, ISSN 1019 7168, Editors-in-Chief John C. Mason and Charles A. Micchelli.

Volume 1, No. 1, 1993

pp. 1-37: Continuous refinement equations and subdivision
W. Dahmen & C. A. Micchelli

pp. 39-60: Preconditioning in implicit initial value problem methods on parallel computers
P. J. van der Houwen

pp. 61-80: Approximation properties of a multilayered feedforward artificial neural network
H. N. Mhaskar

pp. 81-108: Hunting for homoclinic orbits in reversible systems: a shooting technique
A. R. Champneys & A. Spence

pp. 109-126: Wavelet bases for a set of commuting unitary operators
T.N.T. Goodman, S. L. Lee & W. S. Tang

Software notes

pp. 127-137: Sparse matrix multiplication package (SMMP)
R. E. Bank & C. C. Douglas

Volume 1, No. 2, 1993

pp. 139-171: Knot insertion algorithms for piecewise polynomial spaces determined by connection matrices
P. J. Barry, R. N. Goldman & C. A. Micchelli

pp. 173-196: Shape preserving representations and optimality of the Bernstein basis
J.M. Carnicer & J.M. Pena

pp. 197-214: Wavelet-compression and nonlinear n-widths
R.A. DeVore, G. Kyriazis, D. Leviatan & V. M. Tikhomirov

pp. 215-221: Subdivision algorithms with nonnegative masks generally converge
D. E. Gonsor

pp. 223-239: Error bounds for the finite element approximation of a degenerate quasilinear parabolic variational inequality
W.B. Liu & J.W. Barrett

pp. 241-258: Construction of polynomials that are orthogonal with respect to a discrete bilinear form
L. Reichel

Volume 1, No. 3-4, 1993

pp. 259-335: Wavelet approximation methods for pseudodifferential equations II: Matrix compression and fast solution
W. Dahmen, S. Prossdorf and R. Schneider

pp. 337-356: Eigenvalues of the discretized Navier-Stokes equation with application to the detection of Hopf bifurcations
K.A. Cliffe, T.J. Garratt and A. Spence

pp. 357-366: Least squares and Chebyshev fitting for parameter estimation in ODEs
J. Williams and Z. Kalogiratou

pp. 367-394: Parallel continuous Runge-Kutta methods and vanishing lag delay differential equations
C.T.H. Baker and C.A.H. Paul

Volume 2, No.1, 1994, special issue on "Geometric Modeling" edited by Phillip Barry

pp. 1-21: NURBS approximation of surface / surface intersection curves
C.L. Bajaj and G. Xu

pp. 23-40: Elastic curves on the sphere
G. Brunnett and P.E. Crouch

pp. 41-66: Pythagorean-hodograph space curves
R.T. Farouki and T. Sakkalis

pp. 67-80: A weak condition for the convexity of tensor-product Bezier and B-spline surfaces
M.S. Floater

pp. 81-99: Least squares surface approximation to scattered data using multiquadratic functions
R. Franke, H. Hagen and G.M. Nielson

pp. 101-122: Triangular finite elements of HCT type and class Cr
M. Laghchim-Lahlou and P. Sablonniere

pp. 123-142: Helix splines as an example of affine Tchebycheffian splines
H. Pottmann and M.G. Wagner

pp. 143-154: Convergence of subdivision and degree elevation
H. Prautzsch and L. Kobbelt

Volume 2, No.2, 1994

pp. 155-184: Numerical solution of eigenvalue problems for Hamiltonian systems
M. Marletta

pp. 185-214: Continuous two-scale equations and dyadic wavelets
C.K. Chui and X. Shi

pp. 215-222: Some remarks on completely vectorizing point Gauss-Seidel while using the natural ordering
C.C. Douglas

pp. 223-234: A lacunary interpolation algorithm on arbitrary points
E. Venturino

pp. 235-250: Wachspress type rational complex planar splines of degree (3,1)
H.P. Dikshit, A. Ojha and R.A. Zalik

Software notes

pp. 251: Table-based tests for Bessel function software
A.J. Macleod

Volume 2, No. 3, 1994

pp. 261-277: A parallel implementation of the restarted GMRES iterative algorithm for nonsymmetric systems of linear equations
R. Dias da Cunha and T. Hopkins

pp. 279-317: Time-marching numerical schemes for the electric field integral equation on a straight thin wire
P.J. Davies and D.B. Duncan

pp. 319-341: Acceleration property for the E-algorithm and an application to the summation of series
M. Prevost

pp. 343-355: Hankel operators and best Hankel approximation on the half-plane
X. Li

Volume 2, No. 4, 1994

pp. 357-373: Parallel globally adaptive quadrature on the KSR-1
J.M. Bull and T.L. Freeman

pp. 375-391: A planar minimax algorithm for analysis of co-ordinate measurements
D. Zwick

pp. 393-405: The solution of orthogonal Procrustes problems for a family of orthogonally invariant norms
G.A. Watson

pp. 407-436: Numerical methods for eighth-, tenth- and twelfth-order eigenvalue problems arising in thermal instability
E.H. Twizell, A. Boutayeb and K. Djidjeli

pp. 437-459: Convexity of parametric Bezier surfaces in terms of Gaussian curvature signatures
Z. Cheng and C.K. Chui

pp. 461-477: A general extrapolation procedure revisited
C. Brezinski and M. Redivo-Zaglia

pp. 479-491: On local and global sigma-pi neural networks. A common link
B. Lenze

Volume 3, No. 1-2, 1995

pp. 1-22: Two-scale symbol and autocorrelation symbol for B-splines with multiple knots
G. Plonka

pp. 23-40: Perturbed collocation and symplectic RKN methods
G. Ramaswami

pp. 41-58: An algebraic approach to approximate evaluation of a polynomial on a set of real points
V.Y. Pan

pp. 59-88: An introduction to second degree forms
P. Maroni

pp. 89-100: A unified approach to B-spline recursions and knot insertion, with application to new recursion formulas
G. Walz

pp. 101-113: A mixed finite element for the Stokes problem using quadrilateral elements
M. Farhloul and M. Fortin

pp. 115-135: Evaluation of a boundary integral representation for the conformal mapping of the unit disk onto a simply-connected domain
S.N. Chandler-Wilde, J. Levesley and D.M. Hough

pp. 137-145: Characterization of compactly supported refinable splines
W. Lawton, S.L. Lee and Z. Shen

pp. 147-170: Curve design with rational Pythagorean-hodograph curves
H. Pottmann

Volume 3, No. 4, 1995

pp. 309-342: Subdivision schemes in Lp spaces
R.-Q. Jia

pp. 343-352: A new stepsize strategy for explicit Runge-Kutta codes
G. Hall

pp. 353-368: A generalization of de Boor's stability result and symmetric preconditioning
K. Jetter and J. Stoeckler

pp. 369-374: The polynomial topological complexity of Fatou-Julia sets
C.T. Chong

pp. 375-394: A generalization of the variation diminishing property
J.M. Carnicer, T.N.T. Goodman and J.M. Pena

pp. 393-404: Multivariate convexity preserving interpolation by smooth functions
J.M. Carnicer

pp. 405-424: Control curves and knot insertion for trigonometric splines
P.E. Koch, T. Lyche, M. Neamtu and L.L. Schumaker


Numerical stability of biorthogonal wavelet transforms
F. Keinert

Numerical solution of the incompressible Navier--Stokes equations by Krylov subspace and multigrid methods
S. Zeng, C. Vuik and P. Wesseling

On divergence-free wavelets
K. Urban

Sparse-grid finite-volume multigrid for 3D-problems
P.W. Hemker

A two-level additive Schwarz preconditioner for the stationary Stokes equations
S.C. Brenner

Analysis of preconditioning and multigrid for Euler flows with low-subsonic regions
B. Koren and B. van Leer

Multilevel preconditioning -- Appending boundary conditions by Lagrange multipliers
A. Kunoth

Tensor product type subspace splittings and multilevel iterative methods for anisotropic problems
M. Griebel and P. Oswald

Volume 4, No. 3, 1995

pp. 207-260: On multivariate Hermite interpolation
T. Sauer and Y. Yu

pp. 261-282: Convergence estimates for the wavelet-Galerkin method: superconvergence at the node points
S.M. Gomes

pp. 283-292: Compactly supported positive definite radial functions

Volume 4, No. 4, 1995

pp. 293-330: Wavelets on irregular meshes
F. Plantevin

pp. 331-356: Multilevel preconditioning on the refined interface and optimal boundary solvers for the Laplace equation
B.N. Khoromskij and S. Proessdorf

pp. 357-388: On the construction of wavelets on a bounded interval
G. Plonka, K. Selig and M. Tasche

pp. 389-396: Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
H. Wendland

Volume 5, No. 1, 1996

pp. 1-14: Parallel factorization of banded linear matrices using a systolic array processor
I.J. Anderson and S.K. Harbour

pp. 15-30: The analysis of multigrid algorithms for cell centered finite difference methods
J.H. Bramble, R.E. Ewing, J.E. Pasciak and J. Shen

pp. 31-50: Reconstruction of signals from multiscale edges
M.L. Varas S.

pp. 51-94: Spherical wavelet transform and its discretization
W. Freeden and U. Windheuser

pp. 95-124: Analytic wavelets generated by radial functions
C.K. Chui, J. Stoeckler and J.D. Ward

Volume 5, No 2, 1996

Hybrid misclassification minimization
C. Chen and O.L. Mangasarian

Chebyshev approximation by discrete superposition. Application to neural networks
M. Nees

Networks and closed balls
J.L. Noakes

Hyperbolic sigma-pi neural network operators for compactly supported continuous functions
B. Lenze

Some remarks on greedy algorithms
R.A. DeVore and V.N. Temlyakov

Nonlinearity creates linear independence
Y. Ito

Solvable models of layered neural networks based on their differential structure
S. Watanabe

Limitations of the approximation capabilities of neural networks with one hidden layer
C.K. Chui, X. Li and H.N. Mhaskar

Critical points for least-squares problems involving certain analytic functions, with applications to sigmoidal nets
E.D. Sontag

Linear unlearning for cross-validation
L.K. Hansen and J. Larsen

Volume 6, No. 1, 1996

pp. 1-24: Iterative methods for solving Ax = b, GMRES/FOM versus QMR/BiCG
Jane Cullum

pp. 25-45: Bivariate segment approximation and splines
G. Meinardus, G. Nürnberger and G. Walz

pp. 47-64: Numerical solution of Cauchy-type integral equations of index
Jose A. Cuminato

pp. 65-76: A collocation method for singularly perturbed two-point boundary value problems with splines in tension
Miljenko Marusic and Mladen Rogina

pp. 77-86: Complexity reduction of least squares problems involving special Vandermonde matrices
T. Tommasini

pp. 87-96: Interpolation regions for convex cubic curve segments
Jörg Peters

Volume 6, No. 2, 1996

pp. 97-108: Barycentric coordinates for convex polytopes
Joe Warren

pp. 109-138: A finite element method for interface problems in domains with smooth boundaries and interfaces
James H. Bramble and J. Thomas King

pp. 139-157: Derivative corrections for quadrature formulas
William F. Ford, Yuesheng Xu and Yunhe Zhao

pp. 159-189: A subspace preconditioning algorithm for eigenvector/eigenvalue computation
James H. Bramble, Joseph E. Pasciak and Andrew V. Knyazev

pp. 191-206: C^r -finite elements of Powell-Sabin type on the three direction mesh
M. Laghchim-Lahlou and P. Sablonniere

Volume 6, no. 3-4, 1996

E. H. Twizell

Foreword: JOHN CRANK
Jack Howlett

JOHN CRANK: his association with Brunel University
J. C. Newby

pp. 207-226: A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type
J. Crank and P. Nicolson

pp. 227-242: Atmospheric diffusion: some new mathematical models
P. C. Chatwin, D. M. Lewis and N. Mole

pp. 243-262: Galerkin methods for a semilinear parabolic problem with nonlocal boundary conditions
G. Fairweather and J. C. Lopez-Marcos

pp. 263-279: The stability of boundary conditions for an angled-derivative difference scheme
K. W. Morton and N. A. Burgess

pp. 281- 293: The role of the Crank-Gupta model in the theory of free and moving boundary problems
J. R. Ockendon

pp. 295-308: The role of the Crank-Gupta model in the theory of free and moving boundary problems
K. A. Pericleous, M. Cross, G. Moran, P. Chow and K. S. Chan

pp. 309-323: Towards adaptive finite element schemes for partial differential Volterra equation solvers
Simon Shaw and J. R. Whiteman

pp. 325-331: Mathematical modelling of binder removal from plastically-formed engineering ceramics
J. H. Song, M. J. Edirisinghe and J. R. G. Evans

pp. 333-352: Second-order, L_0-stable methods for the heat equation with time-dependent boundary conditions
E. H. Twizell, A. B. Gumel and M. A. Arigu

pp. 353-363: Time-stepping algorithms for semidiscretized linear parabolic PDEs based on rational approximants with distinct real poles
D. A. Voss and A. Q. M. Khaliq

Volume 7, No. 1-2, 1997, Special Issue: Parallel methods for ODEs

pp. 1-31: Parallel methods for ODEs
Kevin Burrage

pp. 5-26: Parallel ODE solvers based on block BVMs
Pierluigi Amodio and Luigi Brugnano

pp. 27-36: A parallel stiff ODE solver based on MIRKs
Claus Bendtsen

pp. 37-57: Parallel iterated methods based on multistep Runge-Kutta methods of Radau type
K. Burrage and H. Suhartanto

pp. 59-77: Parallel iterated method based on multistep Runge-Kutta of Radau type for stiff problems
K. Burrage and H. Suhartanto

pp. 79-96: Order and stability of parallel methods for stiff problems
J. C. Butcher

pp. 97-133: DIMSEMs - diagonally implicit single-eigenvalue methods for the numerical solution of stiff ODEs on parallel computers
Robert F. Enenkel and Kenneth R. Jackson

pp. 135-156: Remarks on the optimal convolution kernel for CSOR waveform relaxation
Min Hu, Ken Jackson, Jan Janssen and Stefan Vandewalle

pp. 157-181: Parallel linear system solvers for Runge-Kutta methods
P. J. van der Houwen and J. J. B. de Swart

pp. 183-197: Waveform relaxation methods for implicit differential equations
P. J. van der Houwen and W. A. van der Veen

Volume 7, No. 3, 1997

pp. 199-233: The Petrov--Galerkin method for second kind integral equations II: multiwavelet schemes
Zhongying Chen, Charles A. Micchelli and Yuesheng Xu

pp. 235-259: Adaptive finite element for semi-linear convection--diffusion problems
L. Pouly and J. Pousin

pp. 261-277: Error analysis of mixed finite elements for cylindrical shells
Geng Yang, Michel C. Delfour and Michel Fortin

pp. 279-294: The compass (star) identity for vector-valued rational interpolants
P.R. Graves-Morris and B. Beckermann

pp. 295-301: Sensitivity analysis of the differential matrix Riccati equation based on the associated linear differential system
Mihail Konstantinov and Vera Angelova

pp. 303-335: A new theoretically motivated higher order upwind scheme on unstructured grids of simplices
Monika Wierse

pp. 337-360: Interior estimates for a low order finite element method for the Reissner--Mindlin plate model
Douglas N. Arnold and Xiaobo Liu

pp. 361-382: Stepsize selection for tolerance proportionality in explicit Runge--Kutta codes
M. Calvo, D.J. Higham, J.I. Montijano and L. Rández

pp. 383-399: Spectral properties of matrix continuous refinement operators
Qingtang Jiang and S.L. Lee

pp. 401-428: Orthogonality properties of linear combinations of orthogonal polynomials II
Francisco Marcellan, Franz Peherstorfer and Robert Steinbauer

Volume 7, No. 4, 1997

pp. 429-454: Spectral factorization of Laurent polynomials
Tim N.T. Goodman, Charles A. Micchelli, Giuseppe Rodriguez and Sebastiano Seatzu

pp. 455-545: Regularity of multiwavelets
C.A. Micchelli and Thomas Sauer

pp. 547-571: Discrete qualocation methods for logarithmic-kernel integral equations on a piecewise smooth boundary
Y. Jeon, I.H. Sloan, E.P. Stephan and J. Elschner

pp. 573-592: Numerical treatment of retarded differential--algebraic equations by collocation methods
R. Hauber

pp. 593-621: Distances between oriented curves in geometric modeling
Przemyslaw Bogacki, Stanley Weinstein and Yuesheng Xu

Volume 8, No. 1-2, 1998

pp. 1-17: Affine frames, quasi-affine frames, and their duals
Charles K. Chui, Xianliang Shi and Joachim Stoeckler

pp. 19-31: Numerical integration of 2-D integrals based on local bivariate C1 quasi-interpolating splines
C. Dagnino and P. Lamberti

pp. 33-48: Numerical solution of generalized Lyapunov equations
Thilo Penzl

pp. 49-63: Invariant smoothness measures for surfaces
Even Mehlum and Christian Tarrou

pp. 65-96: An almost monotone approximation for a nonlinear two-point boundary value problem
Ben-yu Guo and Yuan-ming Wang

pp. 97-110: Parallel implementation of the p-version of the finite element method for elliptic equations on a shared-memory architecture
Tadeusz J. Janik

pp. 111-135: Fast computations with the harmonic Poincare--Steklov operators on nested refined meshes
Boris N. Khoromskij and Siegfried Proessdorf

Volume 8, No. 3, 1998

pp. 137-163 Stability results for scattered-data interpolation on Euclidean spheres
F.J. Narcowich, N. Sivakumar and J.D. Ward

pp. 165-177 Nonlinear corner-cutting
Lyle Noakes

pp. 179-192 On the fast approximation of some nonlinear operators in nonregular wavelet spaces
J. Liandrat and Ph. Tchamitchian

pp. 193-219 On a vector q-d algorithm
D.E. Roberts

pp. 221-247 Symmetric orthonormal scaling functions and wavelets with dilation factor 4
Bin Han

pp. 249-265 The best m-term approximation and greedy algorithms
V.N. Temlyakov

pp. 267-289
Formal vector orthogonal polynomials

Volume 8, No. 4, 1998

pp. 291-315 Vandermonde type determinants and blossoming
Marie-Laurence Mazure

pp. 317-334 The Cayley transform in the numerical solution of unitary differential systems
F. Diele, L. Lopez and R. Peluso

pp. 335-344 Experiments in stepsize control for Adams linear multistep methods
David R. Willé

pp. 345-352 The dual basis functions for the Bernstein polynomials
Bert Jüttler

pp. 353-366 The Cr-fundamental splines of Clough--Tocher and Powell--Sabin types for Lagrange interpolation on a three direction mesh
Mohammed Laghchim-Lahlou

pp. 367-380 Minimal cubature formulae for a family of radial weight functions
Yuan Xu

pp. 381-399 Convergence order estimates of meshless collocation methods using radial basis functions
Carsten Franke and Robert Schaback

Volume 9, No. 1-2, 1998

Kendall Atkinson and Yuesheng Xu

pp 1-20: Numerical exploitation of symmetry in integral equations
Eugene L. Allgower and Kurt Georg

pp 21-35: Recursive generation of the Galerkin--Chebyshev matrix for convolution kernels
Davis K. Cope

pp 37-67: Observations on the numerical stability of the Galerkin method
Allan G. Dallas, G.C. Hsiao and R.E. Kleinman

pp 69-95: The method of fundamental solutions for elliptic boundary value problems
Graeme Fairweather and Andreas Karageorghis

pp 97-115: New boundary element formulas for the biharmonic equation
Youngmok Jeon

pp 117-129: An acceleration method for integral equations by using interpolation post-processing
Qun Lin, Shuhua Zhang and Ningning Yan

pp 131-144: The preconditioned GMRES method for systems of coupled FEM-BEM equations
Patrick Mund and Ernst P. Stephan

pp 145-171: Multiwavelet approximation methods for pseudodifferential equations on curves. Stability and convergence analysis
Siegfried Prössdorf and Jörg Schult

pp 173-190: Multi-parameter extrapolation methods for boundary integral equations
Ulrich Rüde and Aihui Zhou

pp 191-216: The construction of some efficient preconditioners in the boundary element method
O. Steinbach and W.L. Wendland

pp 217-232: Second-kind integral formulations of the capacitance problem
Johannes Tausch and Jacob White

pp 233-249: Wavelet-based preconditioners for boundary integral equations
Thanh Tran, Ernst P. Stephan and Stefan Zaprianov

Volume 10, No.2, 1999

pp. 115-133 Runge--Kutta--Nyström-type parallel block predictor--corrector methods
Nguyen Huu Cong, Karl Strehmel, Rüdiger Weiner and Helmut Podhaisky

pp. 135-167 Optimal discrete and continuous mono-implicit Runge--Kutta schemes for BVODEs
P.H. Muir

pp. 169-186 A class of modified block SSOR preconditioners for symmetric positive definite systems of linear equations
Zhong-Zhi Bai

pp. 187-208 A Chebyshev polynomial method for line integrals with singularities
J.C. Mason and E. Venturino

pp. 209-217 Degree estimates for Ck-piecewise polynomial subdivision surfaces
Hartmut Prautzsch and Ulrich Reif

Volume 12, Nos. 2-3, 2000

pp. 95-131 On the detection of singularities of a periodic function
H.N. Mhaskar and J. Prestin

pp. 133-149 Some results for a class of generalized polynomials
Serena Morigi and Marian Neamtu

pp. 151-174 A fast matrix-vector multiplication method for solving the radiosity equation
Kendall Atkinson and David Da-Kwun Chien

pp. 175-187 Asymptotic convergence of degree-raising
Michael S. Floater and Tom Lyche

pp. 189-211 Parameterization of m-channel orthogonal multifilter banks
Qingtang Jiang

pp. 213-227 Weak greedy algorithms
V.N. Temlyakov

pp. 229-250 Diagonally implicit Runge-Kutta methods for 3D shallow water applications
P.J. van der Houwen and B.P. Sommeijer

pp. 251-259 Convergence of Galerkin method solutions of the integral equation for thin wire antennas
Bryan P. Rynne

pp. 261-272 Modified Mini finite element for the Stokes problem in R2 or R3
Yongdeok Kim and Sungyun Lee

Submissions of articles and proposals for special issues are to be addressed to the Editors-in-Chief:

John C. Mason
School of Computing & Mathematics
University of Huddersfield
Huddersfield HD1 3DH


Charles A. Micchelli
Mathematical Sciences Department
IBM Research Center
P.O. Box 218
Yorktown Heights NY 10598
E-mail: cam@yktvmz.bitnet

Requests for free specimen copies and orders for Advances in Computational Mathematics are to be sent to: E-mail:

Last modified March 20, 2000 Douglas N. Arnold,