Abstract
This paper proposes three different ways of applying a vector extrapolation method to a slow converging vector sequence to accelerate the convergence. The solution of this vector sequence is used to solve an algebraic Riccati equation in transport theory. A numerical example is presented to compare the three applications.
Highlights
The nuclear disaster that occurred in japan on March 2011 emphasizes the vulnerability of the population at the vicinity of the nuclear power plant
This paper proposes three different ways of applying a vector extrapolation method to a slow converging vector sequence to accelerate the convergence
Nonsymmetric algebraic Riccati equations arise in many fields such as transport theory when dealing with particle transfer, nuclear physics, control theory, etc
Summary
The nuclear disaster that occurred in japan on March 2011 emphasizes the vulnerability of the population at the vicinity of the nuclear power plant. An important problem is computing limits of high dimension vector sequences. Many of these sequences converge extremely slowly to their limits. Such vector sequences may arise for example from finite-difference or finite-element discretizations of continuum problems. In such problems, as the mesh sizes decrease, their speed of convergence gets worse. Other vector sequences may result from iterative solution of linear or nonlinear systems of equations. This requires the use of convergence acceleration methods. These techniques transform a sequence of vectors generated by some process to a new one that converges faster than the initial sequence
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