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Orthogonal Polynomials
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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