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Some Physical Applications of the Solution of Ill-conditioned Systems of Linear Equations by J.J. Torsti; A.M. Aurela is a Physics and Astronomy article available to read on EtoBox.

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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 ## AX=B, FXe~G(l) and H(PX-R)~0, h~J=(_l)kaj!, 'k-i <J~lkW) 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 spec

Who reads Some Physical Applications of the Solution of Ill-conditioned Systems of Linear Equations?

Author

J.J. Torsti; A.M. Aurela

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0010-4655)

Published

1972

Language

EN

Field

Physics and Astronomy (Physical Sciences)