Analytical solution of generalized spectral problem in the method of recalculating boundary conditions for a biharmonic equation

An iterative algorithm with an efficient preconditioner for the numerical solution of an elastic problem in approximation of plate theory with mixed boundary conditions is proposed and substantiated. Exact constants of energy equivalence for optimization of iteration method are obtained. Inversion of the preconditioner is equivalent to the double inversion of a discrete analog of the Laplace operator with the Dirichlet boundary conditions.