A Simple Introduction to Numerical Analysis: Volume 2: Interpolation and Approximation
Approximation techniques are widely used in mathematics and applied physics, as exact solutions are frequently impossible to obtain. A Simple Introduction to Numerical Analysis, Volume 2: Interpolation and Approximation extends the first volume to consider problems in interpolation and approximation. Topics covered include the construction of interpolating functions, the determination of polynomial and rational function approximations, numerical quadrature, and the solution of boundary value problems in ordinary differential equations. As with the previous volume, the text is integrated with a software package that allows the reader to work through numerous examples. It is also possible to use the software to consider problems that are beyond the scope of the text. The authors' expertise in combining text and software has resulted in a very readable work.
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Analytical approximation for exp(x B-splines basis functions bottom window Chebyshev approximation Chebyshev polynomials Chebyshev series coefficients collocation Computational consider construct continuous function cubic approximation cubic spline data points decimal places default degree of precision derivative determine differential equation divided differences edit/inspect equally spaced points error function estimate evaluate example Exercise finite Fourier series Gaussian given gives input integral integrand interpolating polynomial interpolation points interval Lagrangian polynomial least squares approximation linear equations Load the program matrix maximum error method minimax approximation minimax error minimax polynomial Neville's algorithm Newton-Cotes Newton-Cotes formulae Notice number of points obtain orthogonal plot polynomial approximation polynomial of degree possible press RETURN produce program APPROX program INTERP prompt Option quadratic spline quadrature formula rational approximation recurrence relation Remes algorithm screen shown in figure Simpson's rule solution tabular points tabular values Taylor series Taylor series expansion theorem tion trapezium rule zeros
Page 174 - This series of computer illustrated texts covers mathematics, science and engineering courses at advanced secondary school, college and university levels. A computer illustrated text is a textbook with integrated software. In a CIT the normal flow of explanation using conventional printed text is reinforced by computer software which can illustrate concepts both literally through graphics and figuratively by example. Computer graphics are very good at conveying a general qualitative understanding...