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Unformatted text preview: B 2 ,i ( t ) and determine its values and the values oF B 2 ,i ( t ) and B 2 ,i ( t ) at the appropriate nodes. 5.2.b . Derive the Formula oF the quintic B-spline B 5 ,i ( t ) and determine its values and the values oF B 5 ,i ( t ) and B 5 ,i ( t ) at the appropriate nodes. Problem 5.3 Consider a set oF equidistant mesh points, x k = x + kh , 0 k m . 5.3.a . Determine a cubic spline b i ( x ) that satises the Following conditions: b i ( x j ) = b iF j < i-1 or j > i + 1 1 iF j = i b i ( x ) = b i ( x ) = 0 For x = x i 2 and x = x i +2 (or simplicity, you may assume that 2 < i < m-2.) 1 5.3.b . Show that b i ( x ) = 0 when | x-x i | 2 h . 5.3.c . Show that b i ( x ) > 0 when | x-x i | < 2 h . 5.3.d . What is the relationship between the spline, b i ( x ), and a B-spline? 2...
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This note was uploaded on 11/10/2011 for the course MAD 5404 taught by Professor Gallivan during the Spring '11 term at FSU.
- Spring '11