Computing Methods, Volume 1Computing Methods, Volume I generalizes and details the methods involved in computer mathematics. The book has been developed in two volumes; Volume I contains Chapters 1 to 5, and Volume II encompasses Chapters 6 to 10. |
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a₁ absolute error accuracy approximate number approximate quantities arbitrary best approximation calculate Chebyshev Chebyshev polynomials coefficients Consequently consider continuous function convergence decimal places defined denote derivatives differentiation divided differences elements equal equation estimate exact value example expression f(xo finite differences forward interpolation formula function f(x Gauss formulae Hence Hermite interpolation Hm(x improper integrals inequality integrand interval irremovable error Lagrange formula Lagrange interpolation polynomial linearly independent Ln(x mathematical maximum absolute error method multipliers nodes numerical integration formulae obtain order differences P₁(x Pn(x Po(x points of interpolation points xo polation polynomial of degree problem produce r.m.s. error R₁ relative errors required to find residual term result satisfy significant digits sin sin sin space substitute t(t² theorem trigonometrical polynomial vanish whilst wn(x x-xo x₁ Y₁ zero π π