lecture 5

# lecture 5 - CE 30125 - Lecture 5 LECTURE 5 INTRODUCTION TO...

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CE 30125 - Lecture 5 p. 5.1 LECTURE 5 INTRODUCTION TO INTERPOLATION • Interpolation function: a function that passes exactly through a set of data points . • Interpolating functions to interpolate values in tables • In tables, the function is only specified at a limited number or discrete set of indepen- dent variable values (as opposed to a continuum function). • We can use interpolation to find functional values at other values of the independent variable, e.g. sin(0.63253) x sin( x ) 0.0 0.000000 0.5 0.479426 1.0 0.841471 1.5 0.997495 2.0 0.909297 2.5 0.598472

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CE 30125 - Lecture 5 p. 5.2 • In numerical methods, like tables, the values of the function are only specified at a discrete number of points! Using interpolation, we can describe or at least approximate the function at every point in space. • For numerical methods, we use interpolation to • Interpolate values from computations • Develop numerical integration schemes • Develop numerical differentiation schemes • Develop finite element methods • Interpolation is typically not used to obtain a functional description of measured data since errors in the data may lead to a poor representation. • Curve fitting to data is handled with a separate set of techniques
CE 30125 - Lecture 5 p. 5.3 Linear Interpolation • Linear interpolation is obtained by passing a straight line between 2 data points = the exact function for which values are known only at a discrete set of data points = the interpolated approximation to the data points (also referred to as interpolation points or nodes) • In tabular form: y f(x 1 ) 0 ) x 0 x 1 f(x) x g(x) fx () gx x 0 , x 1 = x o o x x 1 1

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CE 30125 - Lecture 5 p. 5.4 • If is a linear function then (1) where and are unknown coefficients • To pass through points and we must have: (2) (3)
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## This note was uploaded on 03/02/2012 for the course CE 30125 taught by Professor Westerink,j during the Fall '08 term at Notre Dame.

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lecture 5 - CE 30125 - Lecture 5 LECTURE 5 INTRODUCTION TO...

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