DOOLITTLE

It is always possible to factor a square matrix into a lower triangular matrix and an upper triangular matrix. That is, [A] = [L][U]

Doolittle’s method provides an alternative way to factor A into an LU decomposition without going through the hassle of Gaussian Elimination.

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For a general n×n matrix A, we assume that an LU decomposition exists, and write the form of L and U explicitly. We then systematically solve for the entries in L and U from the equations that result from the multiplications necessary for A=LU.