7 Interpolation 7.1 Interpolation 7.2 Existence, Uniqueness, and Conditioning 7.3 Polynomial Interpolation 7.3.1 Monomial Basis 7.3.2 Lagrange Interpolation 7.3.3 Newton Interpolation 7.3.4 Orthogonal Polynomials 7.3.5 Interpolating Continuous Functions 7.4 Piecewise Polynomial Interpolation 7.4.2 Cubic Spline Interpolation 3 Linear Least Squares 3.1 Linear Least Squares Problems 3.2 Existence and Uniqueness 3.2.1 Normal Equations 3.2.2 Orthogonality and Orthogonal Projectors 6 Optimization 6.1 Optimization Problems 6.2 Existence and Uniqueness 6.2.1 Convexity 6.2.2 Unconstrained Optimality Conditions 6.4 Optimization in One Dimension 6.4.1 Golden Section Search 6.4.3 Newton's Method 6.5 Unconstrained Optimization 6.5.2 Steepest Descent