![]() ![]() I have invented over 100,000 different types of Geddes series and have named each type after the mathematicians whose historic contributions made this work possible (e.g., Geddes-Newton-Laplace series). Finite Difference Method for Partial Differential EquationsĪppendix C: Numerical Analysis Software PackagesĬ.In my PhD thesis, I introduced a vast new family of infinite series expansions for multivariate functions, which I named "Geddes series" in honor of my thesis supervisor. ![]() Numerical Solution of Ordinary Differential EquationsĨ.1 Theory of Differential Equations: An IntroductionĨ.1.2 Stability of the Initial Value ProblemĨ.3 Convergence Analysis of Euler's MethodĨ.4 Numerical Stability, Implicit MethodsĨ.7.1 Higher-Order Differential EquationsĨ.8 Finite Difference Method for Two-Point Boundary Valueĩ. Numerical Linear Algebra: Advanced Topicsħ.1.1 The Linear Least Squares Approximationħ.1.2 Polynomial Least Squares Approximationħ.2.3 The Nonsymmetric Eigenvalue ProblemĨ. Solution of Systems of Linear EquationsĦ.2.5 Solvability Theory of Linear SystemsĦ.4.1 Compact Variants of Gaussian EliminationĦ.4.3 MATLAB Built-in Functions for Solving Linear SystemsĦ.6.1 Jacobi Method and Gauss-Seidel Methodħ. Numerical Integration and Differentiationĥ.2.1 An Asymptotic Estimate of the Trapezoidal Errorĥ.4.1 Differentiation Using Interpolationĥ.4.2 The Method of Undetermined Coefficientsĥ.4.3 Effects of Error in Function ValuesĦ. ![]() The text introduces core areas of numerical analysis and scientific computing along with basic themes of numerical analysis such as the approximation of problems by simpler methods, the construction of algorithms, iteration methods, error analysis, stability, asymptotic error formulas, and the effects of machine arithmetic.Ģ.1.1 Accuracy of Floating-Point RepresentationĢ.1.3 Consequences for Programming of Floating-PointĢ.2 Errors: Definitions, Sources, and ExamplesĢ.3.1 Propagated Error in Function Evaluationģ.3.2 Comparison of Newton and Secant Methodsģ.4.1 Aitken Error Estimation and ExtrapolationĤ.1.6 Newton's Divided Difference Interpolation FormulaĤ.3.2 Construction of the Interpolating Natural Cubic SplineĤ.3.3 Other Interpolating Spline FunctionsĤ.4.1 Accuracy of the Minimax ApproximationĤ.7.2 Solving for the Least Squares ApproximationĤ.7.3 Generalizations of Least Squares Approximationĥ. ![]() Now updated and revised, this significant revision features reorganized and rewritten content, as well as some new additional examples and problems. Offering a clear, precise, and accessible presentation, complete with MATLAB programs, this new Third Edition of Elementary Numerical Analysis gives students the support they need to master basic numerical analysis and scientific computing. ![]()
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