Numerical methods for simultaneous diagonalization
SIAM Journal on Matrix Analysis and Applications
Jacobi Angles for Simultaneous Diagonalization
SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)
Exploiting the symmetry in the parallelization of the Jacobi method
Parallel Computing - Special double issue on environment and tools for parallel scientific computing
Efficient schemes for nearest neighbor load balancing
Parallel Computing - Special issue on parallelization techniques for numerical modelling
Joint Approximate Diagonalization of Positive Definite Hermitian Matrices
SIAM Journal on Matrix Analysis and Applications
Dynamic ordering for a parallel block-Jacobi SVD algorithm
Parallel Computing - Parallel matrix algorithms and applications
On the Problem of Scheduling Flows on Distributed Networks
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Dynamic load balancing by diffusion in heterogeneous systems
Journal of Parallel and Distributed Computing
Topographic Independent Component Analysis
Neural Computation
IEEE Transactions on Signal Processing
Blind source separation based on time-frequency signalrepresentations
IEEE Transactions on Signal Processing
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A new algorithm is described for distributed joint diagonalization of real symmetric or complex Hermitian matrices. The approach, which is based on the Jacobi diagonalization, utilizes distribution of the computational power and memory space, minimizes the communication costs, and runs on clusters of personal computers. It further combines two-step load balancing algorithm with a standard Kalman filter to enable quick but low-cost adaptation to resource varying conditions. Theoretical analysis of its performance shows that the communication costs (when normalized by computational costs) decline linearly with the number and size of the diagonalized matrices. This is also confirmed by experimental results: the measured speedup ratio yields 42.2 when jointly diagonalizing 800 matrices of size 400×400 on a cluster of 50 personal computers.