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lecture29

# lecture29 - CMPSC/MATH 451 Numerical Computations Lecture...

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CMPSC/MATH 451 Numerical Computations Lecture 29 October 28, 2011 Prof. Kamesh Madduri

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Class Overview: Interpolation B-splines (section 2) Octave tutorial, continued Non-linear equations review (see slides in ‘Exam’ folder) 2
Interpolation Polynomial Interpolation Piecewise Polynomial Interpolation Piecewise Polynomial Interpolation Hermite Cubic Interpolation Cubic Spline Interpolation B-splines B-splines form basis for family of spline functions of given degree B-splines can be defined in various ways, including recursion (which we will use), convolution, and divided differences Although in practice we use only finite set of knots t 1 , . . . , t n , for notational convenience we will assume infinite set of knots · · · < t - 2 < t - 1 < t 0 < t 1 < t 2 < · · · Additional knots can be taken as arbitrarily defined points outside interval [ t 1 , t n ] We will also use linear functions v k i ( t ) = ( t - t i ) / ( t i + k - t i ) Michael T. Heath Scientific Computing 51 / 56

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Interpolation Polynomial Interpolation
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lecture29 - CMPSC/MATH 451 Numerical Computations Lecture...

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