This year, we wind up BIT with a selection of papers from our regular stream of contributions. I note that now we have quite a few manuscripts in the Approximation area, both geometric design and numerical cubature, as well as some contributions to Numerical Linear Algebra. Only one paper deals with properties of time stepping methods for differential equations. But rest assured, more is coming up next year!
These are the papers:
Assyr Abdulle, Gilles Vilmart, and Konstantinos Zygalakis investigate the stability properties of integrators for Itô stochastic differential equations. They derive a singly diagonally implicit Runge Kutta method of weak second order, and compares its stability region to existing variants. Mean square and asymptotic stability is considered, as well as different variants of A stability.
A.K.B. Chand and P. Viswanathan study shape preservation aspects of cubic Hermite fractal interpolation functions. They get a desirable shape by putting constraints on values of function and derivative at the knot points. Scaling factors in the subintervals are chosen, to force the function to stay inside a rectangle.
Raffaele D’Ambrosio, Ernst Hairer, and Christophe J. Zbinden study long term integration of a conservative dynamical system. They prove that G-symplecticity of a general linear method implies conjugate-symplecticity of the underlying one step method.
Catterina Dagnino, Paola Lamberti, and Sara Remogna construct new cubature rules for 3D integrals, based on spline quasi-interpolants, expressed as linear combinations of scaled and translated boxes and local linear functionals. Nodes and weights are given, as well as error bounds.
Erik Martin-Dorel, Guillaume Melquiond, and Jean-Michel Muller study floating point computation in the practically interesting case where some parts of the computation are done in a higher precision than the original data. These computations are often a part of a much larger process, and then predictability is of importance, in order to get reliable bounds on the error imposed.
Ralf Hiptmair, Carlos Jerez-Hanckes, and Christoph Schwab study the Maxwell cavity source problem in the frequency domain. They use discretization by means of sparse tensor edge elements, in the case when a full tensor product gives rise to a basis of too high a dimension.
Tsung-Ming Huang, Zhongxiao Jia, and Wen-Wei Lin project a quadratic eigenvalue problem on a subspace, giving Ritz approximations to eigenvalues and eigenvectors. When the angle between an eigenvector and the subspace gets small, the Ritz values converge to the eigenvalue. They introduce the use of refined Ritz vectors which are proved to converge towards an eigenvector.
Zhongxiao Jia and Qian Zhang do a systematic study on how to choose drop tolerance to obtain a sparse approximative inverse, to be used in a preconditioned iterative algorithm for a nonsymmetric linear system.
Shishun Li and Zhengda Huang consider multigrid methods for nonselfadjoint elliptic problems, using a Hermitian/skew-Hermitian splitting as smoother. These iterations converge uniformly, even without a full elliptic regularity assumption, provided that the mesh size of the coarsest grid is sufficiently small, independent of the number of levels.
Marie-Laurence Mazure studies rational functions used for computer aided geometric design. They form an extended Chebyshev space that can be built up by a basis of quotients between Bernstein polynomials. This establishes a relation between Chebyshev spaces good for design and rational functions based on them, and offers new insights on rational Bézier curves.
Yujie Zhang and Yangfeng Su describe a two-level orthogonalization Arnoldi process to reduce a high dimensional delay system into a reduced order delay system. It needs less memory than the standard method, which is based on linear Arnoldi.
Referees
It is a recurring pleasure for me to acknowledge all of you that have helped us to keep the quality and readability of BIT. As is our custom, the referee of each paper is unknown to the author, yet we are all the ones that form, what we use to call the BIT family. Thank you all, editors, referees, and publishers for another good year with BIT!
These are the referees that I found in the files of BIT this year. Forgive me if I have missed someone that properly should deserve to be here:
Ben Adcock
Ravi P Agarwal
Pierluigi Amodio
Andreas Asheim
Winfried Auzinger
Gerard Awanou
Lori Badea
Zhong-Zhi Bai
Johnathan M Bardsley
Domingo Barrera
Roland Becker
Bernhard Beckermann
John Belward
Sergio Blanes
Peter Blomgren
Paola Boito
Matthias Bollhöfer
J. P. Boyd
Richard P Brent
Evelyn Buckwar
Kevin Burrage
Pamela Burrage
Albrecht Böttcher
Marco Caliari
Felix Carbonell Gonzáles
Andrea Censi
Bilal Chanane
Philippe Chartier
Snorre H. Christiansen
Julianne Chung
Emil M. Constantinescu
Tobias Damm
Eric Darrigrand
Oleg Davydov
Johan De Villiers
Kristian Debrabant
Vittoria Demichelis
Weihua Deng
Josef Dick
Luca Dieci
Marco Donatelli
Cedric Effenberger
Yuli Eidelman
Lars Eldén
Jinyan Fan
Lihong Feng
Mahadevan Ganesh
Asghar Ghorbani
Oliver Gibary
Ron Goldman
Hector Gomez
Willy Govaerts
Ivan Graham
Andreas Griewank
Volker Grimm
Nicola Guglielmi
Hongbin Guo
Weihong Guo
Johnny Guzman
Mert Gürbüzbalaban
Stefan Güttel
Wolfgang Hackbusch
Thomas Hagstrom
Ernst Hairer
Harri Hakula
Xuli Han
Martin Hanke
Elias Helou
Johan Helsing
Holger Heumann
Nicholas Higham
Inmaculada Higueras
Martin Hutzenthaler
Johan Håstad
Zdzislaw Jackiewicz
Carlo Janna
Elias Jarlebring
Jae-Hun Jung
Mika Juntunen
Lars Karlsson
Linda Kaufman-Grabiner
Eamonn Keogh
Esther Klann
Peter E Kloeden
Othmar Koch
Plamen Koev
Efi Kokiopoulou
Richard Kowar
Rolf Krause
Natasa Krejic
Ming-Jun Lai
Bishnu Lamichhane
Stig Larsson
Stephen Lau
Richard Lehoucq
Daniel Lesnic
Ren-Cang Li
Shijun Liao
Yongdo Lim
Thorsten Linss
Qiaohua Liu
Maria Maciel
Scott MacLachlan
Alexander Malyshev
Håkon Marthinsen
Gunnar Martinsson
Stefano Maset
Marie-Laurence Mazure
Robert McLachlan
William McLean
Gerard Medioni
Karl Meerbergen
Christian Mehl
Gerard Meurant
Ronald Mickens
Vladimir Mityushev
Juan Monterde
Julio Moro
James Nagy
Yuji Nakatsukasa
Andreas Neuenkirch
Hong Diep Nguyen
Harald Niederreiter
Touray Nikazad
Jan Nordström
Eugene O’Riordan
Peeter Oja
Sheehan Olver
Alexander Ostermann
Brynjulf Owren
Jose M. Peña
Rodrigo Platte
Helmut Podhaisky
Helmut Pottman
Weifeng Qiu
Ronny Ramlau
Joachim Rang
Nils Henrik Risebro
Mickael Robbe
Lucia Romani
Miroslav Rozloznik
Siegfried M. Rump
Paul Sablonnière
Miloud Sadkane
Ahmed Salam
Berkant Savas
Valeriu Savcenco
Achim Schaedle
Othmar Scherzer
Dominik M Schoetzau
Gabriela Schranz-Kirlinger
Simon Shaw
Qin Sheng
Alexandra Smirnova
Mark Spijker
Ernst Stephan
Hai-Wei Sun
Magnus Svärd
Lukas Szpruch
Gustaf Söderlind
Xue-Cheng Tai
Münevver Tezer Sezgin
Tianhai Tian
Francoise Tisseur
Stanimir Tomov
Ninoslav Truhar
Warwick Tucker
Miroslav Tuma
Stefan Turek
Andre Uschmajew
Marnix Van Daele
Robert A van de Geijn
Martin Van Gijzen
Erik Van Vleck
Lieven Vandenberghe
Bart Vandereycken
Wim Vanroose
Stephen Vavasis
Martin Vohralik
Matthias Voigt
Junping Wang
David S Watkins
Yimin Wei
J.A.C. Weideman
Brendt Wohlberg
Jianlin Xia
Chuanju Xu
Chao Yang
Qianqian Yang
Antonella Zanna
Shangyou Zhang
Thank you all and see you later in BIT,
Axel Ruhe
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ruhe, A. Preface to BIT 53:4. Bit Numer Math 53, 821–825 (2013). https://doi.org/10.1007/s10543-013-0456-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10543-013-0456-y