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Low-rank block structures arise in matrices from integral equations,boundary element methods,and discretized PDEs.We will show that,both in theory and in practice,the hierarchically semi-separable(HSS)structured factorization is an effective way of exploiting the low-rankness.It provides a powerful tool for solving linear equations,both dense and sparse,with arithmetic and memory complexity asymptotically lower than the standard methods.It can be parallelized well on modern manycore parallel machines.