Premium
A Block–Stodola eigensolution technique for large algebraic systems with non‐symmetrical matrices
Author(s) -
Dong Stanley B.
Publication year - 1977
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620110204
Subject(s) - eigenvalues and eigenvectors , mathematics , algebraic number , algebra over a field , subspace topology , block (permutation group theory) , linear algebra , quadratic equation , reduction (mathematics) , basis (linear algebra) , krylov subspace , iterative method , pure mathematics , algorithm , combinatorics , mathematical analysis , physics , geometry , quantum mechanics
A Block–Stodola eigensolution method is presented for large algebraic eigensystems of the form AU = λ BU where A is real but non‐symmetric. The steps in this method parallel those of a previous technique for the case when both A and B were real and symmetric. The essence of the technique is simultaneous iteration using a group of trial vectors instead of only one vector as is the case in the classical Stodola–Vianello iteration method. The problem is then transformed into a subspace where a direct solution of the reduced algebraic eigenvalue problem is sought. The main advantage is the significant reduction of computational effort in extracting a subset of eigenvalues and corresponding eigenvectors. Theorems from linear algebra serve to underlie the basis of the present technique. Complex eigendata that emerge during iteration can be handled without doubling the size of the problem. Higher order eigenvalue problems are reducible to first order form for which this technique is applicable. The treatment of the quadratic eigenvalue problem illustrates the details of this extension.