- 1 Let T 1 0 0 1 Denote A Subdivision Of 1 1 Into Two Equal Subintervals And Consider The Space Of Linear S 1 (29.52 KiB) Viewed 29 times
1. Let T = {(-1,0), (0.1]} denote a subdivision of (-1,1) into two equal subintervals and consider the space of linear s
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1. Let T = {(-1,0), (0.1]} denote a subdivision of (-1,1) into two equal subintervals and consider the space of linear s
1. Let T = {(-1,0), (0.1]} denote a subdivision of (-1,1) into two equal subintervals and consider the space of linear splines S = P.(T) n°((-1,1]). Consider the following piecewise linear polynomials defined on the subdivision T: SI 5(1-x), re|-1,0), 01(x) = I € (0,1), NI HOT 02(x) = 1 = 1-3 kall, 1€ (-1,1), 21, (] 03:2) = (x re(-1,0), (1+x), [0, 1]. NI- (b) Show that the set {01(2), 02(2), 03(x)} is linearly independent. Explain why it is a basis set for S.
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