Approximation Techniques for Engineers

Cover -- Half Title -- Title Page -- Copyright Page -- Contents -- Preface to the second edition -- Preface -- Acknowledgments -- About the author -- I: Data approximations -- 1 Classical interpolation methods -- 1.1 Newton interpolation -- 1.1.1 Equidistant Newton interpolation -- 1.1.2 Computational example -- 1.2 Lagrange interpolation -- 1.2.1 Equidistant Lagrange interpolation -- 1.2.2 Computational example -- 1.2.3 Parametric Lagrange interpolation -- 1.3 Hermite interpolation -- 1.3.1 Computational example -- 1.4 Interpolation of functions of two variables with polynomials -- References -- 2 Approximation with splines -- 2.1 Natural cubic splines -- 2.1.1 Equidistant natural spline approximation -- 2.1.2 Computational example -- 2.2 Bezier splines -- 2.2.1 Rational Bezier splines -- 2.2.2 Computational example -- 2.3 Approximation with B-splines -- 2.3.1 Computational example -- 2.3.2 Nonuniform B-splines -- 2.3.3 Nonuniform rational B-splines -- 2.4 Surface spline approximation -- 2.4.1 Coons surfaces -- 2.4.2 Computational example -- 2.4.3 Bezier surfaces -- 2.4.4 Triangular surface patches -- 2.4.5 Computational example -- References -- 3 Least squares approximation -- 3.1 The least squares principle -- 3.2 Linear least squares approximation -- 3.3 Polynomial least squares approximation -- 3.4 Computational example -- 3.5 Exponential and logarithmic least squares approximations -- 3.6 Nonlinear least squares approximation -- 3.6.1 Computational example -- 3.7 Trigonometric least squares approximation -- 3.7.1 Computational example -- 3.8 Directional least squares approximation -- 3.9 Weighted least squares approximation -- References -- 4 Approximation of functions -- 4.1 Least squares approximation of functions -- 4.2 Approximation with Legendre polynomials -- 4.2.1 Gram-Schmidt orthogonalization -- 4.2.2 Computational example