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...Preliminary remarks gaussianelimination choice of pivot applications direct methods for solving systems linear equations they are all over the place numerical programming i cse hans joachim bungartz pageof systemsoflinearequations another important eld application is algebra that deals with problems numerically matrix vector product nding eigenvalues here solution e a rn n b j nd x r mit major signicance omnipresent in numerics interpolation construction cubic spline interpolant see section boundary value bvp ordinary differential ode chapter partial pde terms problem given one distinguishes between full matrices number non zero values same order magnitude as entries o sparse zeros clearly dominate typically oro nlog those often have certain sparsity pattern diagonal tridiagonal ai general band structure c etc which simplies system bandwidth block onedistinguishes different approaches solvers provide exact modulo rounding errors covered this indirect start rst approximation and compute...