Sequences of transformations and triangular recursion schemes, with applications in numerical analysis

Keywords

Mathematics, Recursion (computer science), Reciprocal, Recurrence relation, Generalization

References

• Generalized neville type extrapolation schemesT. Håvie — 1979
• A general extrapolation algorithmClaude Brezinski — 1980
• Extrapolation methods - theory and practiceJet Wimp, Claude Brezinski, Michela Redivo‐Zaglia — 1993
• Extrapolation methods for vector sequencesDavid A. Smith, William F. Ford, Avram Sidi — 1987
• Recursive interpolation, extrapolation and projection *Claude Brezinski — 1983
• Padé-type approximation and general orthogonal polynomialsClaude Brezinski — 1980
• Some results about vector extrapolation methods and related fixed-point iterationsK. Jbilou, H. Sadok — 1991
• Lower estimates for the error of best uniform approximationGünter Meinardus, G. D. Taylor — 1976
• A contour integral representation of linear extrapolation methodsGuido Walz — 1989
• On Extrapolation Algorithms for Ordinary Initial Value ProblemsWilliam B. Gragg — 1965
• About Henrici's transformation for accelerating vector sequencesH. Sadok — 1990
• Survey of Extrapolation Processes in Numerical AnalysisDuncan Joyce — 1971
• On Calculating B-splinesCarl de Boor — 1972
• Fehlerabschätzungen und Extrapolation mit rationalen Funktionen bei Verfahren vom Richardson-TypusRoland Bulirsch, Josef Stoer — 1964
• Vereinfachte Rekursionen zur Richardson-Extrapolation in SpezialfällenClaus Schneider — 1975
• Effiziente Berechnung spezieller Funktionen mittels asymptotischer Entwicklungen und EliminationsprozedurenGuido Walz — 1988
• Remarks on exponential splines, in particular a contour integral representation of exponential B-splinesGuido Walz, Bruno Brosowski — 1989
• Praktische Mathematik IHelmut Werner — 1975
• Erratum: correction to “extrapolation methods for vector sequences”David A. Smith, W. Ford, A. Sidi — 1988
• Bi-orthogonal polynomialsA. Iserles, S. P. Nørsett — 1985

Cited by

• A generalization of the e-algorithmA. Salam — 1993
• More Results on B-Splines via Recurrence RelationsGünter Meinardus, Guido Walz — 1992
• An iterative algorithm for spline interpolationGuido Walz — 1993
• Generalized divided differences, with applications to generalized B-splinesGuido Walz — 1992
• A hierarchically consistent, iterative sequence transformationHerbert H. H. Homeier — 1994
• Convergence acceleration during the 20th centuryClaude Brezinski — 2000
• Computing ECT-B-splines recursivelyG. Mühlbach, Yuehong Tang — 2005
• Asymptotic expansions and acceleration of convergence for higher order iteration processesGuido Walz — 1991
• A unified approach to B-spline recursions and knot insertion, with application to new recursion formulasGuido Walz — 1995
• Determinantal representations for the J transformationHerbert H. H. Homeier — 1995
• Extrapolation algorithms and Pade´ approximations: a historical surveyClaude Brezinski — 1996
• The polynomial approximation in the finite element methodStefano De Marchı, M. Morandi Cecchi — 1995
• Chebyshev Spaces and Bernstein BasesMarie‐Laurence Mazure — 2005
• Extensions of Drummond's process for convergence accelerationClaude Brezinski, Michela Redivo‐Zaglia — 2010
• De Casteljau's algorithm is an extrapolation methodCarsten Carstensen, G. Mühlbach, G.S. Schmidt — 1995
• A general extrapolation procedure revisitedClaude Brezinski, Michela Redivo‐Zaglia — 1994
• A Schur complement approach to a general extrapolation algorithmClaude Brezinski, M. Redivo Zaglia — 2003
• A unified approach to various orthogonalitiesClaude Brezinski — 1992
• Asymptotic expansions for classical and generalized divided differences including applicationsGuido Walz — 1994
• Extended procedures for extrapolation to the limitClaude Brezinski, Michela Redivo‐Zaglia — 2010

Related papers

• Depth of recursion and the ackermann functionBarry Cornelius, G. H. Kirby — 1975
• The equivalence of bar recursion and open recursionThomas Powell — 2014
• UNESCO first international symposium on methods in agroclimatology, 23rd–30th July, 1966W. H. Hogg — 1967
• Recurrence relations of orthogonal polynomials in H 0 1 and H 0 2Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao — 2015
• Этюд об устранении рекурсииН. В. Шилов — 2018
• Numerical stabilization of recurrence relations with vanishing solutionsHenk F. Arnoldus — 1984
• Recurrence relations for orthogonal rational functionsMiroslav S. Pranić, Lothar Reichel — 2012