scholarly journals Minimum property of condition numbers for the Drazin inverse and singular linear equations

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2685-2691
Author(s):  
Haifeng Ma
Keyword(s):  
Linear Equation ◽  
Small Perturbation ◽  
Linear Equations ◽  
Inverse Solution ◽  
Drazin Inverse ◽  
Condition Numbers ◽  
Perturbation Matrix

For a singular linear equation Ax = b,x ? R(AD), a small perturbation matrix E and a vector ?b are given to A and b, respectively. We then have the perturbed singular linear equation (A+E)~x = b+?b, ~x ? R[(A+E)D]. This note is devoted to show the minimum property of the condition numbers on the Drazin inverse AD and the Drazin-inverse solution ADb.

scholarly journals Profil Berpikir Siswa dalam Menyelesaikan Soal Sistem Persamaan Linear

2019 ◽  
Vol 6 (1) ◽  
pp. 69-84
Author(s):  
K. Ayu Dwi Indrawati ◽  
Ahmad Muzaki ◽  
Baiq Rika Ayu Febrilia
Keyword(s):  
Qualitative Research ◽  
Linear Equation ◽  
Linear Equations ◽  
Equation System ◽  
Mathematical Ability ◽  
System Of Linear Equations ◽  
Mathematics Ability ◽  
Linear Equation System ◽  
Thinking Process ◽  
Descriptive Qualitative

This research aimed to describe the thinking process of students in solving the system of linear equations based on Polya stages. This study was a descriptive qualitative research involving six Year 10 students who are selected based on the teacher's advice and the initial mathematical ability categories, namely: (1) Students with low initial mathematics ability, (2) Students with moderate initial mathematics ability, and ( 3) students with high initial mathematics ability categories. The results indicated that students with low initial mathematical ability category were only able to solve the two-variable linear equation system problems. Students in the medium category of initial mathematics ability and students in the category of high initial mathematics ability were able to solve the problem in the form of a system of linear equations of two variables and a system of three-variable linear equations. However, students found it challenging to solve problems with complicated or unusual words or languages.

Strongly Oscillatory and Nonoscillatory Subspaces of Linear Equations

1975 ◽  
Vol 27 (1) ◽  
pp. 106-110 ◽  
Author(s):  
J. Michael Dolan ◽  
Gene A. Klaasen
Keyword(s):  
Linear Equation ◽  
Linear Space ◽  
Nontrivial Solution ◽  
Linear Equations ◽  
Order Equation ◽  
Third Order ◽  
Nonoscillatory Solutions ◽  
Oscillatory Solutions ◽  
The Third ◽  
All Solutions

Consider the nth order linear equationand particularly the third order equationA nontrivial solution of (1)n is said to be oscillatory or nonoscillatory depending on whether it has infinitely many or finitely many zeros on [a, ∞). Let denote respectively the set of all solutions, oscillatory solutions, nonoscillatory solutions of (1)n. is an n-dimensional linear space. A subspace is said to be nonoscillatory or strongly oscillatory respectively if every nontrivial solution of is nonoscillatory or oscillatory. If contains both oscillatory and nonoscillatory solutions then is said to be weakly oscillatory.

SOLVING LINEAR EQUATIONS IN L-FUNCTIONS

2014 ◽  
Vol 10 (03) ◽  
pp. 569-584
Author(s):  
J. KACZOROWSKI ◽  
A. PERELLI
Keyword(s):  
Functional Equation ◽  
Linear Equation ◽  
Dirichlet Series ◽  
Linear Equations

We describe the solutions of the linear equation aX + bY = cZ in the class of Dirichlet series with functional equation. Proofs are based on the properties of certain nonlinear twists of the L-functions.

scholarly journals Gradient methods for computing the Drazin-inverse solution

2013 ◽  
Vol 253 ◽  
pp. 255-263 ◽  
Author(s):  
Sladjana Miljković ◽  
Marko Miladinović ◽  
Predrag S. Stanimirović ◽  
Yimin Wei
Keyword(s):  
Gradient Methods ◽  
Inverse Solution ◽  
Drazin Inverse

scholarly journals Rate of Convergence of Tikhonov Method of Regularization for Constrained Linear Equations with Operators Having Closed Ranges

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Milojica Jaćimović ◽  
Izedin Krnić ◽  
Oleg Obradović
Keyword(s):  
Linear Equation ◽  
Rate Of Convergence ◽  
Linear Equations ◽  
Tikhonov Method ◽  
Method Of Regularization

We derive the estimates of the rate of convergence of the Tikhonov method of regularization for a constrained operator linear equation. In case that the range of the corresponding operator is closed, the estimate is of the same order as the estimates for a linear equation without constraints.

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