Basic Theory 1.1: Orthogonal polynomials 1.2: Properties of orthogonal polynomials 1.3: Three-term recurrence relation 1.4: Quadrature rules 1.5: Classical orthogonal polynomials 1.6: Kernal polynomials 1.7: Sobolev orthogonal polynomials 1.8: Orthogonal polynomials on the semicircle 1.9: Notes to chapter 1 Computational Methods 2.1: Moment-based methods 2.2: Discretization methods 2.3: Computing Cauchy integrals of orthogonal polynomials 2.4: Modification algorithms 2.5: Computing Sobolev orthogonal polynomials 2.6: Notes to chapter 2 Applications 3.1: Quadrature 3.2: Least squares approximation 3.3: Moment-preserving spline approximation 3.4: Slowly convergent series 3.5: Notes to chapter 3
Walter Gautshi is Professor Emeritus at Purdue University, USA.
'This is the first book on constructive methods for and applications of orthogonal polynomials, and the first available collection of relevant Matlab codes ... The book will be of interest not only to mathematicians and numerical analysts but also to a wide range of scientists and engineers.' * EMS Newsletter *