In this paper, we prove a new identity for the least-square solution of an over-determined set of linear equation Ax = b, where A is an m×n full-rank matrix, b is a column-vector of dimension m, and m (the number of equations) is larger than or equal to n (the dimension of the unknown vector x). Generally, the equations are inconsistent and there is no feasible solution for x unless b belongs t...

Determining the diffusion coefficient based on the solution of the linear inverse problem of the parameter estimation by using the Least-square method is presented. A set of temperature measurements at a single sensor location inside the heat conducting body is required. The corresponding direct problem will be solved by an application of the heat fundamental solution.

In seepage problems, the coefficients of permeability in Laplace equation are usually assumed to be constant vs. both space and time; but in reality these coefficients are variable. In this study, the effect of material deformation due to external loads (consolidation) and variation of head in the consolidation process are considered. For the first case, formulation of kx and ky can be defined ...

A square complex matrix A is called if it can be written in the form EP   1 0 U A U  with U being fixed unitary and 1 A being arbitrary matrix in . We give necessary and sufficient conditions for the existence of the solution to the system of complex matrix equation r r   r EP , AX B XC D   and present an expression of the solution to the system when the solvability conditions are satisf...

This paper presents a new approach for synthesizing flat-top patterns, based on the least-square error criterion. The cost function is formulated according to the amplitude approximation error without phase constraint. The optimal array weight is obtained by using the Levenberg–Marquardt nonlinear optimization algorithm. Simulations are performed to compare the proposed approach with the Woodwa...

in this paper, least square method (lsm) and differential transformation method (dtm) are used to solve the problem of laminar nanofluid flow in a semi-porous channel in the presence of transverse magnetic field. due to existence some shortcomings in each method, a novel and efficient method named ls-dtm is introduced which omitted those defects and has an excellent agreement with numerical sol...

The scaled total least square (STLS) problem, introduced by B.D. Rao in 1997, unifies both the total least square (TLS) and the least square (LS) problems. The STLS problems can be solved by the singular value decomposition (SVD). In this paper, we give a rank-revealing two-sided orthogonal decomposition method for solving the STLS problem. An error analysis is presented. Our numerical experime...