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.

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.

In this paper, the inherited collocation method is introduced to solve the fuzzy differential equations. For this purpose, the so-called inherited LU factorization of matrices and inherited polynomials are used to decompose the extended crisp matrix obtained from the proposed method easily. The examples show the efficiency and importance of this method.

The textit{QIF}  (Quadrant Interlocking Factorization) method of Evans and Hatzopoulos solves linear equation systems using textit{WZ}  factorization. The  WZ factorization can be faster than the textit{LU} factorization  because,  it performs the simultaneous evaluation of two columns or two rows. Here, we present a  method for computing the real and integer textit{WZ} and  textit{ZW} factoriz...

In this article the notions of semi weak orthogonality and semi weak factorization structure in a category $mathcal X$ are introduced. Then the relationship between semi weak factorization structures and quasi right (left) and weak factorization structures is given. The main result is a characterization of semi weak orthogonality, factorization of morphisms, and semi weak factorization structur...

The LU factorization is an important numerical algorithm for solving system of linear equations in science and engineering and is characteristic of many dense linear algebra computations. It has even become the de facto numerical algorithm implemented within the LINPACK benchmark to rank the most powerful supercomputers in the world, collected in the TOP500 website. In this context, the challen...

‘Hierarchical Semi-separable’ matrices (HSS matrices) form an important class of structured matrices for which matrix transformation algorithms that are linear in the number of equations (and a function of other structural parameters) can be given. In particular, a system of linear equations Ax = b can be solved with linear complexity in the size of the matrix, the overall complexity being line...

It is well known that any nonsingular M–matrix admits an LU factorization into M–matrices (with L and U lower and upper triangular respectively) and any singular M–matrix is permutation similar to an M–matrix which admits an LU factorization into M–matrices. Varga and Cai establish necessary and sufficient conditions for a singular M–matrix (without permutation) to allow an LU factorization wit...