โ Scribed by J.J. Torsti; A.M. Aurela
No coin nor oath required. For personal study only.
Various physical problems lead to an ill-conditioned system of equations TX U in which the variancecovariance matrix of the measured Vector Uis known. To facilitate the solution of such equations. the following form of the quadratic optimization problem was introduced: join fQ (X) = XTCX + DX + F X and L fulfil (I) and (II) X,L where the known constraints on the vectors X and L are of the form
Constraints (I) represent conventional bounding equations and boundary planes, while (II) rcpre~entconstraints of a new type which cannot be expressed in the form of fixed boundaries.
As the first application, experimental values of the multiple-scattering constant were calculated in the range 10-100 GeV/c from the preliminary data of the cosmic-ray muon spectrograph MARS in Durham, England. The results confirm the value 21 MeV of the constant. The form of the differential cosmic-ray muon spectrum at high energies was also analysed on the basis of different measurements. As a second application, the method was used for solving the old inversion problem of the heat capacity of crystals. The method gave estimates for the frequency spectrum of lattice vibrations and for the anharmonic contributions to the specific heat in the cases of KCI and Cu. in qualitative agreement with the results obtained by other methods.
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