# Algorithmen - kurz gefasst (German Edition) by Uwe Schöning

By Uwe Schöning

In kompakter shape macht das Buch mit den wesentlichen Themen vertraut, die in einer Vorlesung über Algorithmen behandelt werden. Im Mittelpunkt stehen dabei die verschiedensten sequentiellen Algorithmen, deren Komplexitätsanalyse und allgemeine Algoithmen-Paradigma. Prof. Schöning gelingt es, kurz, konkret und verständlich die wichtigsten algorithmischen Aufgabenstellungen (Selektion, Sortieren, Hashing), Algorithmen auf Graphen, algebraische und zahlentheoretische Verfahren zu behandeln. Hinzu kommen heuristische Algorithmenprinzipien wie z.B. genetisches Programmieren.

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**Example text**

K 2 − 1 (with K 1 > N1 and K 2 > N2 ). t. vec H (H(ωk1, ωk2 ))a M1 ,M2 (ωk1 , ωk2 ) = 1, via cyclic optimization [42]. 32) 22 SPECTRAL ANALYSIS OF SIGNALS For the initialization step, we obtain the initial APES estimates of H(ω1 , ω2 ) and α(ω1 , ω2 ) from the available data γ in the following way. Let S be the set of snapshot indices (l 1 , l 2 ) such that the elements of the corresponding initial data snapshot indices {(l 1 , l 2 ), . . , (l 1 , l 2 + M20 − 1), . . , (l + M10 − 1, l 2 ), .

2 Two-Dimensional GAPES Let G be the set of sample indices (n1 , n2 ) for which the data samples are available, and U be the set of sample indices (n1 , n2 ) for which the data samples are missing. The set of available samples {yn1 ,n2 : (n1 , n2 ) ∈ G} is denoted by the g × 1 vector γ, whereas the set of missing samples {yn1 ,n2 : (n1 , n2 ) ∈ U} is denoted by the (N1 N2 − g ) × 1 vector µ. The problem of interest is to estimate α(ω1 , ω2 ) given γ. Assume we consider a K 1 × K 2 -point DFT grid: (ωk1 , ωk2 ) = (2πk 1 / K 1 , 2π k 2 /K 2 ), for k1 = 0, .

The data restoration performance of MAPES-EM is shown in Fig. 3. The missing samples are estimated using the averaging approach we introduced previously. Figs. 3(b) display the real and imaginary parts of the interpolated data, respectively, obtained via MAPES-EM1. Figs. 3(d) show the corresponding results for MAPES-EM2. The locations of the missing samples are also indicated in Fig. 3. The missing samples estimated via the MAPESEM algorithms are quite accurate. More detailed results for MAPES-EM2 are shown in Fig.