Development and Application of Multiple Division Divide-and-Conquer Algorithm for Real Symmetric Eigenproblem

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Numerical linear algebra plays an important role in a large scale numerical simulation in various scientific and technological fields. It is because the core process of the simulation programs are often composed of matrix computations such as linear equation, eigenproblem and singular value decomposition. In this research, we proposed some methods to improve the multiple division divide-and-conquer algorithm for real symmetric eigenproblem, which has been recently proposed by our group. As an application, we established the multiple division divide-and-conquer algorithm for singular value decomposition. Furthermore, we proposed new efficient algorithms to compute Jordan canonical form for square matrices and Kronecker canonical form for matrix pencils.