scholarly journals A fixed-neighbor, distributed algorithm for solving a linear algebraic equation

2013 ◽  
Author(s):  
S. Mou ◽  
A. S. Morse
Keyword(s):  
Algebraic Equation ◽  
Linear Algebraic Equation ◽  
Distributed Algorithm

scholarly journals A Distributed Algorithm for Solving a Linear Algebraic Equation

2015 ◽  
Vol 60 (11) ◽  
pp. 2863-2878 ◽  
Author(s):  
Shaoshuai Mou ◽  
Ji Liu ◽  
A. Stephen Morse
Keyword(s):  
Algebraic Equation ◽  
Linear Algebraic Equation ◽  
Distributed Algorithm

scholarly journals Numerical Solution of Multidimensional Stochastic Itô-Volterra Integral Equation Based on the Least Squares Method and Block Pulse Function

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Ting Ke ◽  
Guo Jiang ◽  
Mengting Deng
Keyword(s):  
Integral Equation ◽  
Error Analysis ◽  
Numerical Solution ◽  
Least Squares ◽  
Algebraic Equation ◽  
Volterra Integral Equation ◽  
Linear Algebraic Equation ◽  
Least Squares Method ◽  
Numerical Examples ◽  
Block Pulse Function

In this paper, a method based on the least squares method and block pulse function is proposed to solve the multidimensional stochastic Itô-Volterra integral equation. The Itô-Volterra integral equation is transformed into a linear algebraic equation. Furthermore, the error analysis is given by the isometry property and Doob’s inequality. Numerical examples verify the effectiveness and precision of this method.

Inhomogeneous Spitzer-type identities for commutative and non-commutative Rota–Baxter algebras

2017 ◽  
Vol 16 (01) ◽  
pp. 1750016
Author(s):  
Gabriel Pietrzkowski
Keyword(s):  
Power Series ◽  
Commutative Ring ◽  
Unique Solution ◽  
Algebraic Equation ◽  
Linear Algebraic Equation

We consider a complete filtered Rota–Baxter (RB) algebra of weight [Formula: see text] over a commutative ring. Finding the unique solution of an inhomogeneous linear algebraic equation in this algebra, we generalize Spitzer’s identity in both commutative and non-commutative cases. As an application, considering the RB algebra of power series in one variable with q-integral as the RB operator, we show certain Eulerian identities.

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