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Errors in Numerical Computation
Systems of Linear Equations
8 other sections not shown
accuracy algorithm arithmetic calculate Chapter Chebyshev polynomials choose clearly coefficients column Consider constant decimal places defined definition denote derivative described determine diagonal differential equation digits divided differences eigenvalues eigenvector elementary reflector elements error bound error term evaluate Example Figure function values Gaussian elimination given by Eq Hence integrating formula interpolation formula interval iterative method Lagrangian Lagrangian interpolating polynomial Legendre-Gauss linear equations LU factorization matrix maximum minimax approximation multiplicity Newton-Cotes formulas Newton-Raphson method nonlinear equations nonzero number of iterations numerical analysis obtain Pade approximation parameters pivoting polynomial of degree problem procedure produce program of Exercise quadratic reader rectangular rule root round-off error rounding error Runge-Kutta methods satisfies secant method simple iteration sinh solve starting values Steffensen's method subintervals subroutine Substituting system of equations system of linear Table tabular points Theorem trapezoidal rule tridiagonal truncation error