What is the concept of matrix factorization in Numerical Analysis?

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What is the concept of matrix factorization in Numerical Analysis?

Matrix factorization in Numerical Analysis refers to the process of decomposing a given matrix into a product of two or more matrices. This decomposition allows for efficient computation of various matrix operations, such as solving systems of linear equations, finding eigenvalues and eigenvectors, and performing matrix inversion. Matrix factorization methods, such as LU decomposition, QR decomposition, and singular value decomposition (SVD), are widely used in numerical algorithms to improve computational efficiency and accuracy.