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In the nonlinear eigenvalue problem of modified Prony method under small perturbations the global convergence of first inverse iteration algorithm of M. Osborne (1970) is investigated.

The features of conductivity in aluminum films produced by various methods are described depending on the presence of impurities, film thickness, and deposition conditions. The results of measuring the surface properties and crystal structure of fabricated films of aluminum, aluminum oxide, and aluminum nitride by X-ray diffraction and atomic force microscopy are presented. SIS, SIN, NIN junctions based on aluminum were fabricated using both shadow evaporation and magnetron sputtering. The current-voltage characteristics were measured. The prospects for improving the characteristics of aluminum SIS junctions, SQUID amplifiers, and SINIS detectors operating at temperatures of about 100 mK are discussed. Keywords: aluminum thin films, surface roughness, atomically smooth films, tunnel junctions.

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