The Best Approximation Method An Introduction - Hromadka, Theodore V. II

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Sommaire:
1. Work Spaces.- 1.1. Metric Spaces.- 1.2. Linear Spaces.- 1.3. Normed Linear Spaces.- 1.4. Banach Spaces.- 2. Integration Theory.- 2.0. Introduction.- 2.1. The Riemann and Lebesgue Integrals: Step and Simple Functions.- 2.2. Lebesque Measure.- 2.3. Measurable Functions.- 2.4. The Lebesgue Integral.- 2.5. Key Theorems in Integration Theory.- 2.6. Lp Spaces.- 2.7. The Metric Space, Lp.- 2.8. Convergence of Sequences.- 2.9. Capsulation.- 3: Hilbert Space and Generalized Fourier Series.- 3.0 Introduction.- 3.1. Inner Product and Hilbert Space (Finite Dimension Spaces).- 3.2. Infinite Dimension Spaces.- 3.3. Approximations in L2(E).- 3.4. Vector Space Representation for Approximations: An Application.- 4. Linear Operators.- 4.0. Introduction.- 4.1. The Derivative as a Linear Operator.- 4.2. Linear Operators.- 4.3. Examples of Linear Operators in Engineering.- 4.4. Linear Operator Norms.- 5. The Best Approximation Method.- 5.0. Introduction.- 5.1. An Inner Product for the Solution of Linear Operator Equations.- 5.2. Orthonormalization Process.- 5.3. Generalized Fourier Series.- 5.4. Approximation Error Evaluation.- 5.5. The Weighted Inner Product.- 6. The Best Approximation Method: Applications.- 6.0. Introduction.- 6.1. Sensitivity of Computational Results to Variation in the Inner Product Weighting Factor.- 6.2. Solving Two-Dimensional Potential Problems.- 6.3. Application to Other Linear Operators.- 6.4. Computer Program: Two-Dimensional Potential Problems Using Real Variable Basis Functions.- 7. Coupling the Best Approximation and Complex Variable Boundary Element Methods.- 7.0. Introduction.- 7.1. The Complex Variable Boundary Element Method.- 7.2. Mathematical Development.- 7.3. The CVBEM and W?.- 7.4. The Space W?A.- 7.5. Applications.- 7.6. Computer Program:Two-Dimensional Potential Problems Using Analytic Basis Functions (CVBEM).- References.- Appendix A: Derivation of CVBEM Approximation Function.- Appendix B: Convergence of CVBEM Approximator.