superlinear convergence rate
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scholarly journals IQN: An Incremental Quasi-Newton Method with Local Superlinear Convergence Rate

2018 ◽  
Vol 28 (2) ◽  
pp. 1670-1698 ◽  
Author(s):  
Aryan Mokhtari ◽  
Mark Eisen ◽  
Alejandro Ribeiro
Keyword(s):  
Convergence Rate ◽  
Newton Method ◽  
Superlinear Convergence ◽  
Local Superlinear Convergence ◽  
Superlinear Convergence Rate ◽  
Quasi Newton

Tri-Diagonal Preconditioner for Toeplitz Systems from Finance

2011 ◽  
Vol 1 (1) ◽  
pp. 82-88
Author(s):  
Hong-Kui Pang ◽  
Ying-Ying Zhang ◽  
Xiao-Qing Jin
Keyword(s):  
Differential Equation ◽  
Theoretical Analysis ◽  
Convergence Rate ◽  
Option Pricing ◽  
Gradient Method ◽  
Preconditioned Conjugate Gradient ◽  
Superlinear Convergence Rate ◽  
Pricing Problems ◽  
Toeplitz Systems ◽  
Toeplitz System

AbstractWe consider a nonsymmetric Toeplitz system which arises in the discretization of a partial integro-differential equation in option pricing problems. The preconditioned conjugate gradient method with a tri-diagonal preconditioner is used to solve this system. Theoretical analysis shows that under certain conditions the tri-diagonal preconditioner leads to a superlinear convergence rate. Numerical results exemplify our theoretical analysis.

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