Matrix factorization


LU Factorization

Nick Higham’s blog

An LU factorization of a \(n \times n\) matrix \(A\) is a factorization \(A = LU\), where \(L\) is lower triangular and \(U\) is upper triangular

LUP factorization

LU factorization with partial pivoting: \(PA = LU\) with \(P\) a permutation matrix.

LDU factorization

Lower-diagonal upper factorization: \(A = LDU\) with \(D\) a diagonal matrix and \(L\) and \(U\) are uni-triangular (triangular with diagonal one).

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