## Spline Analysis |

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### Contents

PIECEWISE LINEAR INTERPOLATION | 10 |

PIECEWISE CUBIC HERMITE INTERPOLATION | 24 |

LINEAR INTEGRAL EQUATIONS | 64 |

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Analysis basis functions bound the right-hand boundary value problems Cauchy-Schwarz Inequality Cholesky decomposition coefficients Computer Corollary defined differential equations Dx(f eigenfunction Euler equation EXERCISES FOR CHAPTER exists a positive finite element finite-dimensional subspace following result fourth-order accurate Galerkin approximations Galerkin method Gaussian elimination hence Hermite interpolation interpolation mapping L2-norm linear system Math mesh length method minimizes Moreover Numerical obtain Peano Kernel Theorem piecewise cubic Hermite piecewise polynomial positive constant positive definite priori bounds priori error bounds problem of finding proof of Theorem prove the following R. S. Varga results of Chapters results of Exercises results of Theorem right-hand side RRG approximation Schultz Second Integral Relation second-order accurate show that if/e spline interpolation strongly coercive sufficiently smooth symmetric Theorem 2.5 triangle inequality tridiagonal matrix uniform partition unique solution variational problem vector space xi+1 xl+1 xl+l