The polynomial interpolation in one dimensional space R is an important method to approximate the functions. The Lagrange and Newton methods are two well known types of interpolations. In this work, we describe the semi inherited interpolation for approximating the values of a function. In this case, the interpolation matrix has the semi inherited LU factorization.

An incomplete factorization method for preconditioning symmetric positive definite matrices is introduced to solve normal equations. The normal equations are formed as a means to solve rectangular matrices from linear least squares problems. The procedure is based on a block incomplete Cholesky factorization and a multilevel recursive strategy with an approximate Schur complement matrix formed ...

Given an n × n symmetric possibly indefinite matrix A, a modified Cholesky algorithm computes a factorization of the positive definite matrix A + E , where E is a correction matrix. Since the factorization is often used to compute a Newton-like downhill search direction for an optimization problem, the goals are to compute the modification without much additional cost and to keep A + E wellcond...

Matrix Factorization and Matrix Concentration by Lester Wayne Mackey II Doctor of Philosophy in Electrical Engineering and Computer Sciences with the Designated Emphasis in Communication, Computation, and Statistics University of California, Berkeley Professor Michael I. Jordan, Chair Motivated by the constrained factorization problems of sparse principal components analysis (PCA) for gene expr...

We present a distributed stochastic gradient descent algorithm for performing low-rank matrix factorization on streaming data. Low-rank matrix factorization is often used as a technique for collaborative filtering. As opposed to recent algorithms that perform matrix factorization in parallel on a batch of training examples [4], our algorithm operates on a stream of incoming examples. We experim...

Using the block vec matrix, I give a necessary and sufficient condition for factorization of a matrix into the Kronecker product of two other matrices. As a consequence, I obtain an elementary algorithmic procedure to decide whether a matrix has a square root for the Kronecker product. Introduction My statistician colleague, J.E. Chacón, asked me how to decide if a real given matrix A has a squ...

In this paper‎, ‎an efficient dropping criterion has been used to compute the IUL factorization obtained from Backward Factored APproximate INVerse (BFAPINV) and ILU factorization obtained from Forward Factored APproximate INVerse (FFAPINV) algorithms‎. ‎We use different drop tolerance parameters to compute the preconditioners‎. ‎To study the effect of such a dropping on the quality of the ILU ...