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Find the LU-decomposition of the 3 x 3 matrix 6 -9 A = 2 5 -3 -4 1 10 The triangular matrices L and U are not uniquely determined by the matrix equation A = LU. These two matrices together contain n2 + n unknown el- ements. Thus when comparing elements on the left- and right-hand side of A = LU we have n2 equations and n? + n unknowns. We require a further n conditions to uniquely determine the matrices. There are three additional sets of n conditions that are commonly used. These are Doolittle's method with ljj = 1, j = 1,...,n; Choleski's method with ljj = ujj, j = 1,..., n; Crout's method with u;j = 1, j = 1,..., n. Apply Crout's method. %3D %3D

Find the LU-decomposition of the 3 x 3 matrix 6 -9 A = 2 5 -3 -4 1 10 The triangular matrices L and U are not uniquely determined by the matrix equation A = LU. These two matrices together contain n2 + n unknown el- ements. Thus when comparing elements on the left- and right-hand side of A = LU we have n2 equations and n? + n unknowns. We require a further n conditions to uniquely determine the matrices. There are three additional sets of n conditions that are commonly used. These are Doolittle's method with ljj = 1, j = 1,...,n; Choleski's method with ljj = ujj, j = 1,..., n; Crout's method with u;j = 1, j = 1,..., n. Apply Crout's method. %3D %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Find the LU-decomposition of the 3 x 3 matrix 6 -9 5 -3 3 A = -4 1 10 The triangular matrices L and U are not uniquely determined by the matrix equation A = LU. These two matrices together contain n² +n unknown el- ements. Thus when comparing elements on the left- and right-hand side of A = LU we have n? equations and n? + n unknowns. We require a further n conditions to uniquely determine the matrices. There are three additional sets of n conditions that are commonly used. These are Doolittle's method with ljj = 1, j = 1,..., n; Choleski's method with ljj = ujj, j = 1,...,n; Crout's method with u;j = 1, j = 1,...,n. Apply Crout's method. %3D %3D
Transcribed Image Text:1. Find the LU-decomposition of the 3 x 3 matrix 6 -9 5 -3 3 A = -4 1 10 The triangular matrices L and U are not uniquely determined by the matrix equation A = LU. These two matrices together contain n² +n unknown el- ements. Thus when comparing elements on the left- and right-hand side of A = LU we have n? equations and n? + n unknowns. We require a further n conditions to uniquely determine the matrices. There are three additional sets of n conditions that are commonly used. These are Doolittle's method with ljj = 1, j = 1,..., n; Choleski's method with ljj = ujj, j = 1,...,n; Crout's method with u;j = 1, j = 1,...,n. Apply Crout's method. %3D %3D
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