Naslov
On the global convergence of the complex HZ method

Autori
Hari, Vjeran

Izvornik
SIAM Journal on Matrix Analysis and Applications (0895-4798) 40 (2019), 4; 1291-1310

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
generalized eigenvalue problem ; Jacobi method ; global convergence

Sažetak
The paper considers a Jacobi method for solving the generalized eigenvalue problem Ax = lambda Bx, where A and B are complex Hermitian matrices and B is positive definite. The method is a proper generalization of the standard Jacobi method for the Hermitian matrix A to the matrix pair (A, B). The paper derives the method and proves its global convergence under the large class of generalized serial pivot strategies. If both matrices are positive definite, it can be implemented as a one-sided method. It then solves the initial problem as the generalized singular value problem. Its main application is to serve as a kernel algorithm in a block Jacobi method for the same problem with large matrices A and B. The block Jacobi methods are methods of choice on contemporary CPU and GPU computing architectures. The proposed algorithm is very efficient on pairs of almost diagonal matrices, and diagonalization of such matrices is the main task of the kernel algorithm. The numerical tests indicate the high relative accuracy of the method on certain pairs of positive definite matrices.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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