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Technical Report WM CS 2006 08 College of William Mary Department of Computer Science WM CS 2006 08 PRIMME PReconditioned Iterative MultiMethod Eigensolver Methods and software description Andreas Stathopoulos November 2006 PRIMME PRECONDITIONED ITERATIVE MULTIMETHOD EIGENSOLVER METHODS AND SOFTWARE DESCRIPTION ANDREAS STATHOPOULOS AND JAMES R MCCOMBS Abstract This paper describes the PRIMME software package for the solving large sparse Hermitian and real symmetric eigenvalue problems The difficulty and importance of these problems have increased over the years necessitating the use of preconditioning and near optimally converging iterative methods On the other hand the complexity of tuning or even using such methods has kept them outside the reach of many users Responding to this problem our goal was to develop a general purpose software that requires minimal or no tuning yet it provides the best possible robustness and efficiency PRIMME is a comprehensive package that brings state of the art methods from bleeding edge to production with a flexible yet highly usable interface We review the theory that gives rise to the near optimal methods GD k and JDQMR and present the various algorithms that constitute the basis of PRIMME We also describe the software implementation interface and provide some sample experimental results 1 Introduction PRIMME or PReconditioned Iterative Multi Method Eigensolver is a software package for the solution of large sparse Hermitian and real symmetric eigenvalue problems We view PRIMME as a significant step toward an industrial strength eigenvalue code for large difficult eigenproblems where it is not possible to factorize the matrix and users can only apply the matrix operator and possibly a preconditioning operator on vectors If the matrix can be factorized the shift invert Lanczos code by Grimes Lewis and Simon has set a high standard for robustness 31 However even in factorizable cases the factorization and back substitutions can be



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