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The aim of this thesis is accelerating the process of calculating generalized eigenvalues of a paired matrix by QZ algorithm and using parallel processing capabilities in this algorithm. We used SuperGlue framework that is a new parallelism framework and also cause a little overhead. the operations of algorithm define as some tasks in SuperGlue and to specify dependencies the framework use data versioning. By this type of specifying dependencies we could perform tasks more efficient. We choose the reduction process to Hessenberg form for parallesion as a part of the algorithm. This process is divided in two part, first part is reduction to block Hessenburg form and then the second part is reduction from block hessenburg to hessenburg form. The first part is just parallelised by new framwork and then the second part is replaced by a new algorithm that is more efficient and parallelised by SuperGlue.
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