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Unformatted text preview: Department of Mathematics University of Houston Numerical Analysis I Dr. Ronald H.W. Hoppe Numerical Analysis I (2nd Homework Assignment) Exercise 5 ( Block Gauss elimination ) Let A ∈ R N × N , N := ∑ m i =1 n i , n i ∈ N , 1 ≤ i ≤ m and b ∈ R N be block structured according to A = A 11 · · · A 1 m A 21 · · · A 2 m · · · · · · · · · · · · · · · A m 1 · · · A mm , b = ( b 1 , · , · , · ,b m ) T , where A ij ∈ R n i × n j , 1 ≤ i,j ≤ m, b i ∈ R n i , 1 ≤ i ≤ m . (i) Consider the solution of the linear algebraic system Ax = b . Use a corresponding structuring of the solution vector x ∈ R N and give a block variant of Gauss elimination. (ii) Give a block variant of the LRdecomposition for block tridiagonal matrices A ∈ R N × N , i.e., A ij = 0 for  i j ≥ 2 , 1 ≤ i,j ≤ m ....
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This note was uploaded on 02/21/2012 for the course ENG 3000 taught by Professor Staff during the Spring '12 term at University of Houston.
 Spring '12
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