Question

True or False: Solving normal equations by LU factorization solves a least squares problem in floating-point arithmetic as accurately as possible.

Answer 1

It is true that solving normal equations by LU Factorization solves a least squares problem in floating point arithmetic as acurately as possible.

In numerical analysis and linear algebra, lower–upper (LU) decomposition or factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix. The product sometimes includes a permutation matrix as well. LU decomposition can be viewed as the matrix form of Gaussian elimination. Computers usually solve square systems of linear equations using LU decomposition, and it is also a key step when inverting a matrix or computing the determinant of a matrix. LU decomposition was introduced by Polish mathematician Tadeusz Banachiewicz in 1938.