HOMEWORK8120202: ESM4A - NUMERICALMETHODSSpring 2009Prof. Dr. Lars LinsenZymantas DarbenasSchool of Engineering and ScienceJacobs UniversityDue: Friday, April 24, 2009 at noon(in the mailbox labeled “Linsen” in the entrance hall of Research I).Problem 22:Spline interpolation.(10 points)(a) Derive the collocation matrix for periodic quadratic spline interpolation using B-spline represen-tations over the knot sequence32,52,72,92,112.(b) Given knotsui=i+ 2fori= 1, . . . ,4, points(p1, . . . , p4) = (1,4,1,3), and endpoint derivativesd1=d4= 1. Use clamped cubic spline interpolation to compute an interpolating spline in B-splinerepresentation. Sketch the graph of the spline curve and the control polygon.Problem 23:Uniform subdivision.(10 points)(a) Given uniform B-splinesNni(u)over knot sequenceZand uniform B-splinesMni(u)over knotsequence12ZwithsummationdisplayiciNni(u) =summationdisplayibniMni(u).Show thatbni=12(bn-1i+bn-1i+1)withb02i=b02i+1=cifor
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Spline interpolation, B-spline, Prof. Dr. Lars Linsen