Introduction to Scientific Computing and Data Analysis
This textbook provides and introduction to numerical computing and its applications in science and engineering. The topics covered include those usually found in an introductory course, as well as those that arise in data analysis. This includes optimization and regression based methods using a singular value decomposition. The emphasis is on problem solving, and there are numerous exercises throughout the text concerning applications in engineering and science. The essential role of the mathematical theory underlying the methods is also considered, both for understanding how the method works, as well as how the error in the computation depends on the method being used. The MATLAB codes used to produce most of the figures and data tables in the text are available on the author’s website and SpringerLink.
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2 Solving A Nonlinear Equation
3 Matrix Equations
4 Eigenvalue Problems
6 Numerical Integration
7 Initial Value Problems
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A-stable According to Theorem algorithm approximation assumed bisection method calculate column computed value condition number converge cubic spline curve data points data set derive determine diagonal differential equation digits double precision eigenvalues eigenvectors error function evaluate exact solution example Exercise explain finite difference floating-point floating-point number flops formula Gaussian given in Table integration rule interpolation function interval inverse iteration ISSN iteration steps iterative error least squares MATLAB matrix equation midpoint rule minimization minimum model function Newton’s method nonlinear nonzero norm Note numerical methods numerical solution obtained orthogonal iteration orthogonal matrix polynomial positive definite possible power method procedure produce Rayleigh quotient iteration requires result satisfies secant method Section shown in Figure Simpson’s rule singular values solve subintervals Suppose symmetric matrix tion trapezoidal rule vector xi+1 y(tj zero