# hw2 - Homework 2 Foundations of Computational Math 1 Fall...

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Homework 2 Foundations of Computational Math 1 Fall 2010 The solutions will be posted on Wednesay, 9/15/10 Problem 2.1 Let n = 4 and consider the lower triangular system Lx = f of the form 1 0 0 0 λ 21 1 0 0 λ 31 λ 32 1 0 λ 41 λ 42 λ 43 1 ξ 1 ξ 2 ξ 3 ξ 4 = φ 1 φ 2 φ 3 φ 4 Recall, that it was shown in class that the column-oriented algorithm could be derived from a factorization L = L 1 L 2 L 3 where L i was an elementary unit lower triangular matrix associated with the i -th column of L . Show that the row-oriented algorithm can be derived from a factorization of L of the form L = R 2 R 3 R 4 where R i is associated with the i -th row of L . Problem 2.2 A ﬁrst order linear recurrence is deﬁned as follows: α 0 = γ 0 α i = β i α i - 1 + γ i i = 1 , ··· , n where α i , γ i , β i are all scalars. 2.2.a

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hw2 - Homework 2 Foundations of Computational Math 1 Fall...

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