scholarly journals Inversion Free Algorithms for Computing the Principal Square Root of a Matrix

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Nicholas Assimakis ◽  
Maria Adam
Keyword(s):  
Riccati Equation ◽  
Newton Method ◽  
Continuous Time ◽  
Iterative Algorithms ◽  
Algebraic Method ◽  
Matrix Inversion ◽  
Square Root ◽  
Special Case ◽  
New Algorithms

New algorithms are presented about the principal square root of ann×nmatrixA. In particular, all the classical iterative algorithms require matrix inversion at every iteration. The proposed inversion free iterative algorithms are based on the Schulz iteration or the Bernoulli substitution as a special case of the continuous time Riccati equation. It is certified that the proposed algorithms are equivalent to the classical Newton method. An inversion free algebraic method, which is based on applying the Bernoulli substitution to a special case of the continuous time Riccati equation, is also proposed.

scholarly journals An Improved Iterative Method for Solving the Discrete Algebraic Riccati Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Li Wang
Keyword(s):  
Optimal Control ◽  
Iterative Method ◽  
Control Systems ◽  
Riccati Equation ◽  
Newton Method ◽  
Iterative Algorithms ◽  
Networked Systems ◽  
Algebraic Riccati Equation ◽  
Numerical Example ◽  
Discrete Algebraic Riccati Equation

The discrete algebraic Riccati equation has wide applications, especially in networked systems and optimal control systems. In this paper, according to the damped Newton method, two iterative algorithms with a stepsize parameter is proposed to solve the discrete algebraic Riccati equation, one of which is an extension of Algorithm (4.1) in Dai and Bai (2011). A numerical example demonstrates the convergence effect of the presented algorithm.

scholarly journals On the square-root method for continuous-time algebraic Riccati equations

1999 ◽  
Vol 40 (4) ◽  
pp. 459-468 ◽  
Author(s):  
Linzhang Lu ◽  
C. E. M. Pearce
Keyword(s):  
Riccati Equation ◽  
Continuous Time ◽  
Riccati Equations ◽  
Algebraic Riccati Equation ◽  
Square Root ◽  
Numerical Examples ◽  
Algebraic Riccati Equations ◽  
Solution Methods ◽  
Square Root Method

AbstractWe give a simple and transparent proof for the square-root method of solving the continuous-time algebraic Riccati equation. We examine some benefits of combining the square-root method with other solution methods. The iterative square-root method is also discussed. Finally, paradigm numerical examples are given to compare the square-root method with the Schur method.

scholarly journals Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach

2021 ◽  
Author(s):  
Yves Achdou ◽  
Jiequn Han ◽  
Jean-Michel Lasry ◽  
Pierre-Louis Lions ◽  
Benjamin Moll
Keyword(s):  
Continuous Time ◽  
Wealth Distribution ◽  
Closed Form Solution ◽  
Form Solution ◽  
Heterogeneous Agent ◽  
Saving Behavior ◽  
Income And Wealth Distribution ◽  
Heterogeneous Agent Models ◽  
Special Case

Abstract We recast the Aiyagari-Bewley-Huggett model of income and wealth distribution in continuous time. This workhorse model – as well as heterogeneous agent models more generally – then boils down to a system of partial differential equations, a fact we take advantage of to make two types of contributions. First, a number of new theoretical results: (i) an analytic characterization of the consumption and saving behavior of the poor, particularly their marginal propensities to consume; (ii) a closed-form solution for the wealth distribution in a special case with two income types; (iii) a proof that there is a unique stationary equilibrium if the intertemporal elasticity of substitution is weakly greater than one. Second, we develop a simple, efficient and portable algorithm for numerically solving for equilibria in a wide class of heterogeneous agent models, including – but not limited to – the Aiyagari-Bewley-Huggett model.

scholarly journals A Generalized Inexact Newton Method for Inverse Eigenvalue Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Weiping Shen
Keyword(s):  
Newton Method ◽  
Quadratic Convergence ◽  
Eigenvalue Problems ◽  
Generalized Newton Method ◽  
Inexact Newton Method ◽  
Numerical Tests ◽  
Inverse Eigenvalue Problems ◽  
Inverse Eigenvalue ◽  
Generalized Newton ◽  
Special Case

We propose a generalized inexact Newton method for solving the inverse eigenvalue problems, which includes the generalized Newton method as a special case. Under the nonsingularity assumption of the Jacobian matrices at the solutionc*, a convergence analysis covering both the distinct and multiple eigenvalue cases is provided and the quadratic convergence property is proved. Moreover, numerical tests are given in the last section and comparisons with the generalized Newton method are made.

Modified Square Root Method of Matrix Inversion

Technometrics ◽  
1962 ◽  
Vol 4 (2) ◽  
pp. 282-287 ◽  
Author(s):  
A. E. Sarhan ◽  
B. G. Greenberg ◽  
Eleanor Rorerts
Keyword(s):  
Matrix Inversion ◽  
Square Root ◽  
Square Root Method

Transient analysis of M/M/1 queues in discrete time by general server vacations

1994 ◽  
Vol 31 (A) ◽  
pp. 115-129 ◽  
Author(s):  
W. Böhm ◽  
S. G. Mohanty
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Transient Analysis ◽  
Queueing System ◽  
Queueing Model ◽  
Discrete Parameter ◽  
Server Vacations ◽  
Special Case ◽  
Combinatorial Methods ◽  
Transient And Steady State

In this contribution we consider an M/M/1 queueing model with general server vacations. Transient and steady state analysis are carried out in discrete time by combinatorial methods. Using weak convergence of discrete-parameter Markov chains we also obtain formulas for the corresponding continuous-time queueing model. As a special case we discuss briefly a queueing system with a T-policy operating.

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