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Autor(en): 
  • Jürgen Gerhard
  • Modular Algorithms in Symbolic Summation and Symbolic Integration 
     

    (Buch)
    Dieser Artikel gilt, aufgrund seiner Grösse, beim Versand als 2 Artikel!


    Übersicht
     
    Lieferstatus:   i.d.R. innert 5-10 Tagen versandfertig
    Veröffentlichung:  2004  
    Genre:  EDV / Informatik 
    ISBN:  9783540240617 
    EAN-Code: 
    9783540240617 
    Verlag:  Springer Berlin Heidelberg 
    Einband:  Kartoniert  
    Sprache:  English  
    Dimensionen:  H 235 mm / B 155 mm / D 13 mm 
    Gewicht:  369 gr 
    Seiten:  240 
    Zus. Info:  Book 
    Bewertung: Titel bewerten / Meinung schreiben
    Inhalt:
    This work brings together two streams in computer algebra: symbolic integration and summation on the one hand, and fast algorithmics on the other hand. In many algorithmically oriented areas of computer science, theanalysisof- gorithms-placedintothe limelightbyDonKnuth'stalkat the 1970ICM -provides a crystal-clear criterion for success. The researcher who designs an algorithmthat is faster (asymptotically, in the worst case) than any previous method receives instant grati?cation: her result will be recognized as valuable. Alas, the downside is that such results come along quite infrequently, despite our best efforts. An alternative evaluation method is to run a new algorithm on examples; this has its obvious problems, but is sometimes the best we can do. George Collins, one of the fathers of computer algebra and a great experimenter,wrote in 1969: "I think this demonstrates again that a simple analysis is often more revealing than a ream of empirical data (although both are important). " Within computer algebra, some areas have traditionally followed the former methodology, notably some parts of polynomial algebra and linear algebra. Other areas, such as polynomial system solving, have not yet been amenable to this - proach. The usual "input size" parameters of computer science seem inadequate, and although some natural "geometric" parameters have been identi?ed (solution dimension, regularity), not all (potential) major progress can be expressed in this framework. Symbolic integration and summation have been in a similar state.

      



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