File:Polynommultiplikation.svg
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DescriptionPolynommultiplikation.svg |
Deutsch: Schnelle Multiplikation zweier Polynome und zu . Dabei werden zunächst die zu den beiden Polynomen und korrespondierenden Koeffizientenfolgen durch schnelle Fourier-Transformation in Laufzeit transformiert, sodass sich die zum Polynom korrespondierende fouriertransformierte Koeffizientenfolgen durch komponentenweise Multiplikation in Laufzeit ergibt. Diese wird schlussendlich durch schnelle inverse Fourier-Transformation in Laufzeit rücktransformiert. Die Gesamtlaufzeit liegt in und ist damit asymptotisch effizienter im Vergleich zur klassischen Polynommultiplikation mit Laufzeit . |
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Source | Own work |
Author | Algomath |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 02:49, 29 March 2020 | 1,276 × 532 (170 KB) | Algomath (talk | contribs) | Vereinheitlichung Schriftbild | |
02:15, 29 March 2020 | 1,276 × 532 (167 KB) | Algomath (talk | contribs) | {{Information |description ={{de|1=Schnelle Multiplikation zweier Polynome <math>p_a(x)=\sum\nolimits_{i=0}^{n} a_i x^i</math> und <math>p_b(x)=\sum\nolimits_{i=0}^{n} b_i x^i</math> zu <math>p_c(x):=p_a(x)\cdot p_b(x)=\sum\nolimits_{i=0}^{n} c_i x^i</math>. Dabei werden zunächst die zu den beiden Polynomen <math>p_a</math> und <math>p_b</math> korrespondierenden Koeffizientenfolgen durch schnelle Fourier-Transformation in Laufzeit <math>\mathcal{O}(n \log n)</math> transformiert, sodass si... |
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