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We investigate the performance of the routines in LAPACK and the Successive Band Reduction (SBR) toolbox for the reduction of a dense matrix to tridiagonal form, a crucial preprocessing stage in the solution of the symmetric eigenvalue problem, on general-purpose multicore processors. In response to the advances of hardware accelerators, we also modify the code in SBR. to accelerate the computation by off-loading a significant part of the operations to a graphics processor (GPU). Performance results illustrate the parallelism and scalability of these algorithms on current high-performance multi-core architectures.