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Spectral Interpolation, Differentiation, Quadrature (PDF) This section provides the lecture notes for the course.
„e word continuous is important: numerical analysis concerns real (or complex) variables, as opposed to discrete variables, which are the domain of computer science. 0.1Direct or iterative methods?
The formulas for numerical differentiation can also be used (this is in fact their major application) to solve, numerically, various types of ordinary and partial differential equations.
Thus the analysis component of ‘numerical analysis’ is essential. We rely on tools of classical real analysis, such as continuity, differentia-bility, Taylor expansion, and convergence of sequences and series. Matrix computations play a fundamental role in numerical analy-sis. Discretization of continuous variables turns calculus into algebra.
Numerical analysis is a branch of Mathematics that deals with devising efficient methods for obtaining numerical solutions to difficult Mathematical problems. Most of the Mathematical problems that arise in science and engineering are very hard and sometime impossible to solve exactly.
1 Solution of equations by iteration. 1.1 Introduction. 1.2 Simple iteration. 1.3 Iterative solution of equations. 1.4 Relaxation and Newton’s method. 1.5 The secant method. 1.6 The bisection method. 1.7 Global behaviour. 1.8 Notes Exercises. 2 Solution of systems of linear equations. 2.1 Introduction. 2.2 Gaussian elimination. 2.3 LU factorisation
1.1 What is Numerical Analysis? . . . . . . . . . . . . . . . . . .3 1.2 An Illustrative Example . . . . . . . . . . . . . . . . . . . . .3 1.2.1 An Approximation Principle . . . . . . . . . . . . . . .4
