Splines and Variational MethodsIntroduction ideas; Lagrangian interpolates; Hermitian interpolates; Polynomial splines and generalizations; Approximating functions of several variables; Fundamentals for variational methods; The finite element method; The method of collocation; Index. |
Contents
Introductory Ideas | 1 |
Lagrangian Interpolates | 24 |
Hermitian Interpolates | 52 |
Copyright | |
8 other sections not shown
Other editions - View all
Common terms and phrases
approximating functions basis best approximation boundary value problem compute constant continuous function continuously differentiable convergence cubic spline cubic spline interpolate defined differential operator error estimates evenly spaced knots example Exercises existence and uniqueness Figure finite element approximate finite element method function f(t Galerkin methods Gårding's inequality given function graph Hermite interpolate Hermite polynomials inequality inner product space interpolation problem interval Lagrange interpolate Lagrange polynomials linear Lagrange polynomials linear operator linear system linearly independent matrix mesh spacing nonsingular normed linear space P₁ partial differential equations particular partition piecewise cubic Hermite piecewise Lagrange polynomial piecewise linear Lagrange piecewise polynomials plane points polynomial of degree polynomial p(x polynomial spline positive definite Proof Rayleigh-Ritz real numbers rectangular grid satisfying Section simple smoothness solution x(t solving the interpolation spline functions spline interpolate t₁ Tchebycheff norm theorem triangle unique solution vectors x₁ zero ди ду