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The calculator will find (if possible) the LU decomposition of the given matrix $$$ A $$$, i.e. such a lower triangular matrix $$$ L $$$ and an upper triangular matrix $$$ U $$$ that $$$ A=LU $$$, with steps shown.
LU Decomposition . After reading this chapter, you should be able to: 1. identify when LU decomposition is numerically more efficient than Gaussian elimination, 2. decompose a nonsingular matrix into LU, and 3. show how LU decomposition is used to find the inverse of a matrix.
LU Decomposition method is used to solve a set of simultaneous linear equations, [A] [X] = [C], where [A]nxn is a non-sin- gular square coefficient matrix, [X] n x1 is the solution vector, and [C] n x1 is the right hand side array.
LU decomposition is a better way to implement Gauss elimination, especially for repeated solving a number of equations with the same left-hand side. That is, for solving the equation Ax b with different values of b for the same A.
LU decomposition, where L is a lower-triangular matrix with 1 as the diagonal elements and U is an upper-triangular matrix. Just as there are many combinations of 12=1⋅12=2⋅6=3⋅4=4⋅3=..., there are infinite number of combinations of L⋅U. However, when the diagonal elements of L are fixed to be 1, the remaining elements are uniquely fixed. A L .
An LU decomposition of a matrix A is the product of a lower triangular matrix and an upper triangular matrix that is equal to A. It turns out that we need only consider lower triangular matrices L that have 1s down the diagonal.
Using an LU decomposition to solve systems of equations. Once a matrix A has been decomposed into lower and upper triangular parts it is possible to obtain the solution to AX = B in a direct way. Given A, find L and U so that A = LU. Hence LUX = B. Let Y = UX so that LY = B. Solve this triangular system for Y .
