Titlebook: Introduction to Scientific Computing and Data Analysis; Mark H. Holmes Textbook 2023Latest edition The Editor(s) (if applicable) and The A

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Eigenvalue Problems,, where . is an . and . is an .. There are a couple of observations worth making about this problem. First, . is always a solution of (.), and so what is of interest are the nonzero solutions. Second, if . is a solution then ., for any number ., is also a solution.

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Solving A Nonlinear Equation,In this chapter, one of the more common mathematical problems is studied, which is to find the solution, or solutions, of an equation of the form .. To illustrate the situation, we begin with a few examples.

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Optimization: Descent Methods,The problem central to this chapter, and the preceding one, is easy to state: given a function ., find the point . where . achieves its minimum value.

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Matrix Equations, .. Together, they are central components of what is called numerical linear algebra. What will be evident from reading this material is the prominent role matrix factorizations play in the subject. To explain what this involves, given a matrix ., one factors it as . or .. The factors, ., ., and .,

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Interpolation,tion from data is one of the central objectives in science and engineering and exactly what or how this is done depends on the particular setting. Two examples are shown in Figure .. Figure .(Left) contains data obtained from measurements of redshift type supernovae. As is often the case with comput