Hilbert space

Method of Boundary States as an Effective Technique of Solving of Heterogeneous Problems of Elasticity Theory

Authors: Penkov V. B., Satalkina L. V.

Method of boundary states in combination with perturbation technique discovers its efficiency on heterogeneous problems of elastostatics. Solutions of problems for body of geometric configuration «peg», produced from heterogeneous material with axisymmetric heterogeneity is performed and illustrated.

Generalization of Method A. A. Dorodnicyn Close Calculation of Eigenvalues and Eigenvectors of Symmetric Matrices on Case of Self-Conjugate Discrete Operators

Authors: Maleko Е. М.

Let the discrete self-conjugate operator A operates in separable Hilbert space H and has the kernel resolvent with simple spectrum. Self-conjugate and limited operator B operates also in H. Then it is possible to find such number ε > 0, that eigenvalues and eigenfunctions of the perturbation operatorA+εB will be calculated on a method of Dorodnicyn.