Mechanisms and Methods of Applied Mathematics in the Works of S.A. Gershgorin

The article examines the works of S.A. Gershgorin (also spelled Gerschgorin) (1901–1933), a Soviet mathematician whose outstanding accomplishments of less than ten years of his scientific life are still being elaborated and cited in leading scientific journals. Gershgorin's early achievements are associated with his inventions: he proposed a way to create a mechanical integrator, a device for solving partial differential equations (Laplace equation). A further development of the grid method proposed by Gershgorin in 1929 was the creation in the USSR of electrical integrators – the analog calculating machines that allowed integrating equations up to the 20th order for a large number of problems in thermal engineering, hydraulics, and elasticity theory. His pioneering method for finding the eigenvalues of a square matrix, the so-called Gershgorin's circles, received worldwide recognition. The article provides a selected bibliography of S.A. Gershgorin's scientific works published from 1924 to 1933.