Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb（萨格勒布大学机械与船舶工程学院）；Department of Mathematics, University of Zagreb（萨格勒布大学数学系）；MSV sustavi d.o.o.（MSV系统有限责任公司）
Sanja Singer, Sasa Singer, Vedran Novakovic, Aleksandar Uscumlic, Vedran Dunjko
We describe two main classes of one-sided trigonometric and hyperbolic Jacobi-type algorithms for computing eigenvalues and eigenvectors of Hermitian matrices. These types of algorithms exhibit significant advantages over many other eigenvalue algorithms. If the matrices permit, both types of algorithms compute the eigenvalues and eigenvectors with high relative accuracy.
We present novel parallelization techniques for both trigonometric and hyperbolic classes of algorithms, as well as some new ideas on how pivoting in each cycle of the algorithm can improve the speed of the parallel one-sided algorithms. These parallelization approaches are applicable to both distributed-memory and shared-memory machines.
The numerical testing performed indicates that the hyperbolic algorithms may be superior to the trigonometric ones, although, in theory, the latter seem more natural.
Three-Level Parallel J-Jacobi Algorithms for Hermitian Matrices
Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb（萨格勒布大学机械与造船工程学院）；Department of Mathematics, University of Zagreb（萨格勒布大学数学系）；Ruđer Bošković Institute（鲁德·博什科维奇研究所）；Multicom d.o.o.（Multicom有限公司）
On the global convergence of the Jacobi method for symmetric matrices of order 4 under parallel strategies
Faculty of Chemical Engineering and Technology, University of Zagreb（萨格勒布大学化学工程与技术学院）；Department of Mathematics, Faculty of Science, University of Zagreb（萨格勒布大学理学院数学系）
Application of the Parallel Dichotomy Algorithm for solving Toeplitz tridiagonal systems of linear equations with one right-hand side
Institute of Computational Mathematics and Mathematical Geophysics（计算数学与数学地球物理研究所）；Budker Institute of Nuclear Physics（布德克核物理研究所）；Novosibirsk State University（新西伯利亚国立大学）
