engleski

A hybrid algorithm for solving shifted linear systems

In this talk, we propose a new algorithm for solving dense shifted linear systems with multiple right-hand sides and a large number of shifts. Such problems arise e.g. in control theory when computing the frequency response of a LTI system, and in many other applications as well. The new algorithm is designed for hybrid computer architectures that use classical multicore processors in combination with GPU accelerators with Nvidia CUDA technology. The algorithm consists of two phases: first, a hybrid CPU-GPU routine is used in order to transform the linear system to a so-called controller--Hessenberg form. This reduction is done only once, regardless of the number of shifts, and allows us to later solve the systems with far less computational effort. In the second phase, the transformed systems are solved by means of a pure GPU algorithm, simultaneously for a large batch of shifts. The solver combines custom made highly parallel kernels with the efficient cuBLAS routines. Such distribution of computational load shows significant performance benefits compared to classical CPU-bound algorithms, which we demonstrate by numerical experiments. This is joint work with Nela Bosner and Zlatko Drmač.

GPU ; Hessenberg matrix ; parallel solver ; shifted linear systems ; transfer function

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