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Convergence of the block Jacobi methods

Vrijeme: 12.5.2021
Predavaonica: vir
Predavač: Erna Begović Kovač, FKIT, University of Zagreb
Naziv: Convergence of the block Jacobi methods

The talk is scheduled in virtual setting, using Zoom platform. The talk will also be live-streamed via YouTube. During the meeting, the questions can be posed via chat or audio for participants in the meeting. Everybody interested is invited to participate in the Zoom meeting, with the limit of 100 participants, or to follow the live-broadcast.

Link to Zoom meeting will be put here few days before the talk.
Link to YouTube live broadcast will be put here 10 min before the talk.

The talk will be in English.

ABSTRACT: Jacobi diagonalization algorithm is an iterative method for computing the eigenvalues and eigenvectors of a matrix.
Given a symmetric matrix $A$, the block Jacobi method generates a sequence of matrices
$$A^{(k+1)}=U_k^TA^{(k)}U_k, k>=0, A^{(0)}=A,$$
where $U_k$ are orthogonal elementary block matrices.

In this talk we will discuss the global convergence of the block Jacobi method for symmetric matrices.
We will introduce a class of generalized serial pivot strategies that is significantly enlarging the known class of weak wavefront strategies and show the global convergence of the method defined by such strategies. The convergence results are phrased in the form
$$S(A')<= cS(A),$$
where $A'$ is the matrix obtained from $A$ after one full cycle of the method, $c<1$ is a constant, and $S(A)$ is the off-diagonal norm of $A$.
The results are generalized using the theory of block Jacobi operators, so they can be used for proving convergence of more general Jacobi-type processes.

This is a joint work with Vjeran Hari.

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