Na bazi novih metoda matematičke optimizacije analizira se stari problem rekonstrukcije Zemljina rotacijskog elipsoida na bazi podataka mjerenja, koji je već početkom 18. stoljeća promatrao francuski ...matematičar i astronom markiz Pierre-Simon de Laplace. Posebno je analizirana, ilustrirana i modificirana efikasna metoda iz rada (Sabo i Scitovski 2009) za traženje optimalnih parametara najbolje l1 linearne aproksimacije. U znanstvenoj literaturi problem procjene najbolje l1 aproksimacije obično se povezuje s imenom hrvatskog znanstvenika J. R. Boškovića. Metode za traženje najbolje l1 aproksimacije u posljednje vrijeme dobivaju novi zamah u različitim tehničkim primjenama zbog svojstva robusnosti i mogućnosti implementacije u realnom vremenu na suvremenim računalima.
Lambeck and Hopgood (1981, 1982) have made a comparative study of spectral characteristics of the angular momentum of atmospheric circulation and fluctuations in the Length-of-Day (LOD) data. The ...Fourier analysis of these data reveals a good correlation between the two processes, including a large spread of power in the range of a 20- to 70-month period. We re-examine here the above two time series by using the Walsh spectral analysis, which seems to be more appropriate for series with sharp peaks and reversals. The comparative study shows that in addition to 12-, 6- and 3-month seasonal terms, the present work discovers statistically significant (90% confidence interval) periods of (i) 26 months (hitherto weakly resolved) associated with a quasibiennial term, and (ii) 40 ± 4 months in both the data. The resolution of the spread components removes meteorological noise uncertainity from astronomical observations of LOD in the study of the excitation mechanism of solid earth.
