Statistische Und Numerische Methoden Der Datenanalyse
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Der Umfang des Datenmaterials in Wissenschaft und Technik nimmt immer schneller zu; seine Auswertung und Beurteilung erweisen sich zunehmend als die eigentliche Schwierigkeit bei vielen wichtigen Problemen. Dem steht auf der anderen Seite ein seit Jahren ungebrochenes Anwachsen der Rechnerleistung und die zunehmende Verf�gbarkeit m�chtiger Algorithmen gegen�ber, aber es ist oft nicht einfach, von diesen Hilfsmitteln den richtigen und professionellen Gebrauch zu machen. Dieses Buch, entstanden aus der Praxis der Verarbeitung gro er Datenmengen, will eine Einf�hrung und Hilfe auf diesem Gebiet geben. Viele der Probleme sind statistischer Natur. Hier ist es sprichw�rtlich leicht, Fehler zu machen. Deshalb sind der Erkl�rung und der kritischen Durchleuch- tung statistischer Zusammenh�nge auch im Hinblick auf die Praxis ein ange- messener Raum gewidmet und ebenso den Monte Carlo-Methoden, welche heute einen verh�ltnism� ig einfachen Zugang zu vielen statistischen Problemen bie- ten. Werkzeuge f�r die Organisation und Strukturierung gro er Datenmengen bilden ein weiteres wichtiges Thema. Dazu geh�ren auch effiziente Verfahren zum Sortieren und Suchen, welche oft Teil gr� erer Algorithmen sind. Die Verarbeitung gro er Datenmengen hat oft die Extraktion verh�ltnism� ig weniger Parameter zum Ziel. Hier sind Verfahren wie die Methoden der klein- sten Quadrate und der Maximum-Likelihood wichtig, in Verbindung mit effek- tiven Optimierungsalgorithmen. Ein weiteres Problem, welches oft untersch�tzt wird, ist die Rekonstruktion urspr�nglicher Verteilungen aus fehlerbehafteten Messungen durch Entfaltung. Mit der Verf�gbarkeit mathematischer Bibliotheken f�r Matrixoperationen k�n- nen viele Probleme elegant in Matrixschreibweise formuliert und aufRechnern gel�st werden. Deswegen werden auch die einfachen Grundlagen der Matrixal- gebra behandelt.
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