An algorithm for the minimum-length least-squares solution of a set of observation equations

Summary A new computer-oriented algorithm GSO is presented for solving overdetermined systems of linear observation equations according to the principle of the least-squares method. The matrix of the system of observation equations may be of deficient rank. In this case the algorithm leads to the vector of unknowns with a minimum Euclidean norm. Alternatively, it is possible to minimize the norm of a subvector formed by a selected group of unknowns. The weight coefficient matrix, corresponding to the vector (subvector) of unknows, has the least possible trace. The algorithm GSO is based on the Gram-Schmidt Orthogonalization of suitably defined augmented matrices. The establishing and solving of normal equations is not necessary. Apart from the unknowns and residuals, GSO also determines the factorized weight coefficient matrices of the adjusted values.Presented at the I.A.G. International Symposium on Optimization of Design and Computation of Control Networks, Sopron, Hungary 1977.     

To the problem of noise reduction in sea-level records used in vertical crustal movement detection

The aim of this investigation is to develop a simple technique that would allow us to use the sea-level records for detecting contemporary vertical crustal movements of duration from several months to several years. The choice of auxiliary data needed for any such analysis is restricted to the regularly available meteorological data to make this approach possible in routine search for precursory movements in earthquake-prone areas. A linear mathematical model is designed to evaluate the effect of atmospheric temperature and pressure variations, river discharge, long periodic tides and Chandlerian motion. Spectra of the residual sea-level variations are also shown. It is concluded that local episodic crustal movements of a magnitude larger than some 10 cm may be detectable by this approach. If finer resolution is needed then it it necessary to also account for steric level, wind, and sea-current variations, for which data are largely non-existent.     

Magnetic properties of natural Mn-oxides

Summary The paper is devoted to the study of the magnetic properties, of the volume magnetic susceptibility in a weak magnetic field, of the specific magnetic susceptibility in a strong magnetic field, of natural remanent magnetization and its stability in A.C. fields, and of the temperature dependence of magnetic susceptibility of natural Mn-oxides. Samples of pyrolusite, polianite, manganite, hausmannite, psilomelan and wad from different localities all over the world were studied; the measured values are statistically treated so that the given values are valid in general. Hausmannite displayed typical values of the magnetic susceptibility, different from the values of the other Mn-oxides. In general, many natural Mn-oxides contain heterogeneous admixtures of Fe-oxides, which are responsible for their ferromagnetic properties. A high degree of magnetic hardness, predetermining the minerals for palaeomagnetic research, was proved with many of the natural Mn-oxides.     

Tensor structure and the least squares

It is shown that for linear parametric adjustment models all the least-squares equations can be obtained from a commutative diagram, where the observation and parameter spaces are regarded as covariant. Their contravariant counterparts are defined through the metric property of the covariance matrix of the observations.     

ТЕОРИЯ ВОЗНИКНОВЕНИЯ КВАЗИДВУХЛЕТНЕГО ЦИКЛА В АТМОСФЕРЕ

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On sweeping frequency impedance measurements

Summary The current spectral density I() dependence on the width of the frequency band and sweep period is studied. The relation between the required accuracy of measurement an the optional parameters of the sweeping process is formulated.     

The response of the total electron content to the interplanetary magnetic sector boundary crossing

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An effective method of frequency analyses of time series of geo-physical quantities

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Relation between the monthly sums of sunshine and global radiation

Summary The statistical treatment of the dependence of monthly sums of global radiation on the monthly sums of sunshine at the stations of Hradec Králové, Bratislava — Koliba and Hurbanovo is presented. The parameters of linear and quadratic regression are derived for the said stations and for the individual months of the year. Drawing on the statistical analysis of the initial data sets, the accuracy and reliability of the mentioned regression relations are critically evaluated.