TU Berlin

Fachgebiet Algorithmische AlgebraProf. Dr. Peter Bürgisser

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Prof. Dr. Peter Bürgisser

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Anschrift
Technische Universität Berlin
Institut für Mathematik
Sekretariat MA 3-2
Straße des 17. Juni 136
10623 Berlin

Büro
Raum MA 317 (3. OG)
Institut für Mathematik

Kontakt

Sekretariat
Beate Nießen
Raum MA 318
Tel.: +49 (0)30 314 - 25771

eMail
peter.buergisser@offmath.tu-berlin.de

Telefon
+49 (0)30 314 - 75902
Faxgerät
+49 (0)30 314 - 25839

Sprechstunde
Während der Vorlesungszeit: Do, 15-16 Uhr.
Während der vorlesungsfreien Zeit: nach Vereinbarung.

Publikationen

Verification complexity of linear prime ideals
Zitatschlüssel BL-Verification-Complexity-Of-Linear-Prime-Ideals
Autor Peter Bürgisser and Thomas Lickteig
Seiten 247-267
Jahr 1992
Journal J. Pure Appl. Alg.
Jahrgang 81
Zusammenfassung The topic of this paper is the complexity of algebraic decision trees deciding membership in an algebraic subset $X$ in $R^m$ where $R$ is a real or algebraically closed field. We define a notion of verification complexity of a (real) prime ideal (in a prime cone) which gives a lower bound on the decision complexity. We exactly determine the verification complexity of some prime ideals of linear type generalizing a result by Winograd (1970). As an application we show uniform optimality with respect to the number of multiplications and divisions needed for two algorithms: For deciding whether a number is a zero of several polynomials - if this number and the coefficients of these polynomials are given as input data - evaluation of each polynomial with Horner's rule and then testing the values for zero is optimal. For verifying that a vector satisfies a system of linear equations - given the vector and the coefficients of the system as input data - the natural algorithm is optimal.
Link zur Publikation Download Bibtex Eintrag

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