Convergence of the complex block Jacobi methods under the generalized serial pivot strategies

Abstract

The paper considers the convergence of the complex block Jacobi diagonalization methods under the large set of the generalized serial pivot strategies. The global convergence of the block methods for Hermitian, normal and $J$-Hermitian matrices is proven. In order to obtain the convergence results for the block methods that solve other eigenvalue problems, such as the generalized eigenvalue problem, we consider the convergence of a general block iterative process which uses the complex block Jacobi annihilators and operators.

Figures (3)

• Figure 1: Convergence of the off-norm on a random Hermitian block matrix $A\in\mathbb{C}^{200\times200}$ under five different generalized serial pivot strategies.
• Figure 2: Convergence of the off-norm on a random Hermitian block matrix $A\in\mathbb{C}^{n\times n}$ with different block sizes.
• Figure 3: Accuracy of the computed eigenvalues on an ill-conditioned Hermitian block matrix $A\in\mathbb{C}^{200\times200}$ with different block sizes.

Theorems & Definitions (15)

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• proof : Proof of the Theorem \ref{['tm:Jacobi-type']}