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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... Orthogonal sets of polynomials 392 2. Recurrence relations for orthogonal polynomials 394 3. The Christoffel - Darboux identity 396 396 4. Properties of orthogonal polynomials § 5. Certain Special Cases of Orthogonal Sets of Polynomials ...
... Orthogonal sets of polynomials 392 2. Recurrence relations for orthogonal polynomials 394 3. The Christoffel - Darboux identity 396 396 4. Properties of orthogonal polynomials § 5. Certain Special Cases of Orthogonal Sets of Polynomials ...
Page 394
... orthogonal polynomials , for instance , that the coefficient for the most significant degree should always be unity , or that it be positive , whilst the norm of the polynomial is unity , the set of orthogonal polynomials in the ...
... orthogonal polynomials , for instance , that the coefficient for the most significant degree should always be unity , or that it be positive , whilst the norm of the polynomial is unity , the set of orthogonal polynomials in the ...
Page 399
... polynomial of degree n - 1 or less . Consequently , R1 ( x ) belongs to an orthogonal set of polynomials with a weight p ( x ) . As we have seen , polynomials of identical degree in two orthogonal sets with the same weight , can only be ...
... polynomial of degree n - 1 or less . Consequently , R1 ( x ) belongs to an orthogonal set of polynomials with a weight p ( x ) . As we have seen , polynomials of identical degree in two orthogonal sets with the same weight , can only be ...
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Common terms and phrases
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