Chapter-10

Chapter-10 - LU Decomposition and Matrix Inversion Chapter...

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LU Decomposition and Matrix Inversion Chapter 10 Provides an efficient way to compute matrix inverse by separating the time consuming elimination of the Matrix [A] from manipulations of the right-hand side {B}. Gauss elimination , in which the forward elimination comprises the bulk of the computational effort, can be implemented as an LU decomposition.

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If L - lower triangular matrix U - upper triangular matrix Then, [A]{X}={B} can be decomposed into two matrices [L] and [U] such that [L][U]=[A] [L][U]{X}={B} Similar to first phase of Gauss elimination , consider [U]{X}={D} [L]{D}={B} [L]{D}={B} is used to generate an intermediate vector {D} by forward substitution Then, [U]{X}={D} is used to get {X} by back substitution.
Fig 10.1

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Fig 10.4
Fig 10.5

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LU decomposition requires the same total FLOPS as for Gauss elimination. Saves computing time by separating time- consuming elimination step from the manipulations of the right hand side.
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