scholarly journals Randomized double and triple Kaczmarz for solving extended normal equations

CALCOLO ◽  
2021 ◽  
Vol 58 (2) ◽  
Author(s):  
Kui Du ◽  
Xiao-Hui Sun
Keyword(s):  
Normal Equations

Structure of the system of normal equations in the construction and equalization of analytical phototriangulation by the ligament method using the coplanarity condition

2020 ◽  
Vol 64 (5) ◽  
pp. 507-514
Author(s):  
Bezmenov V.M. ◽  
Keyword(s):  
Normal Equations

Рассматривается построение и уравнивание аналитической пространственной фототриангуляции, ос- нованной на совместном использованием условия коллинеарности и условия компланарности векторов. Получена структура системы нормальных уравнений. Предлагаемое решение позволяет выполнять по- строение фототриангуляции с одновременным определением (уточнением) элементов внешнего ори- ентирования и внутреннего ориентирования съёмочной камеры. Для назначения начальных значений весов уравнений, составленных с использованием условия компланарности, для некоторой точки ис- следуемого объекта (местности) предлагается использовать ошибки определения пространственных координат точки, рассчитанные методом прямой фотограмметрической засечки для произвольного случая съёмки.

The Estimation of Aquifer Properties From Reservoir Performance in Water-Drive Fields

1977 ◽  
Vol 99 (2) ◽  
pp. 345-352 ◽  
Author(s):  
A. T. Chatas
Keyword(s):  
Least Squares ◽  
Material Balance ◽  
Dimensionless Form ◽  
Simultaneous Solution ◽  
Method Of Least Squares ◽  
Normal Equations ◽  
Aquifer Parameters ◽  
Reservoir Performance ◽  
Analytical Functions ◽  
Aquifer Properties

The purpose of this paper is to indicate a method for estimating values of specified aquifer parameters from an investigation of the reservoir performance of an associated oilfield. To achieve this objective an analysis was made of the simultaneous solution of the material-balance and diffusivity equations, followed by an application of the method of least squares. Three analytical functions evolved, which in dimensionless form were numerically evaluated by computer and tabulated herein. Application of the proffered method requires the simultaneous solution of the three normal equations developed in the paper.

scholarly journals Approximating Sets of Symmetric and Positive-Definite Matrices by Geodesics

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
L. Machado ◽  
F. Silva Leite
Keyword(s):  
Linear Regression ◽  
Riemannian Manifolds ◽  
General Linear Group ◽  
Positive Definite ◽  
Positive Definite Matrices ◽  
Regression Problem ◽  
Natural Action ◽  
Normal Equations ◽  
Linear Regression Problem ◽  
Classical Linear Regression

We formulate a generalized version of the classical linear regression problem on Riemannian manifolds and derive the counterpart to the normal equations for the manifold of symmetric and positive definite matrices, equipped with the only metric that is invariant under the natural action of the general linear group.

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