Parallel Iterative Linear Solvers on GPU: A Financial Engineering Case

2010 ◽  
Author(s):  
Abhijeet Gaikwad ◽  
Ioane Muni Toke
Keyword(s):  
Financial Engineering ◽  
Linear Solvers ◽  
Parallel Iterative ◽  
Iterative Linear Solvers

scholarly journals Parallel iterative linear solvers for multistep Runge-Kutta methods

1997 ◽  
Vol 85 (1) ◽  
pp. 145-167 ◽  
Author(s):  
Eleonora Messina ◽  
Jacques J.B de Swart ◽  
Wolter A van der Veen
Keyword(s):  
Linear Solvers ◽  
Runge Kutta ◽  
Parallel Iterative ◽  
Iterative Linear Solvers

Speed-up of scalable iterative linear solvers implemented on an array of transputers

1995 ◽  
Vol 21 (4) ◽  
pp. 669-682 ◽  
Author(s):  
A. Asenov ◽  
D. Reid ◽  
J.R. Barker
Keyword(s):  
Linear Solvers ◽  
Speed Up ◽  
Iterative Linear Solvers

scholarly journals Consistent treatment of incompletely converged iterative linear solvers in reverse-mode algorithmic differentiation

2020 ◽  
Vol 77 (2) ◽  
pp. 597-616
Author(s):  
Siamak Akbarzadeh ◽  
Jan Hückelheim ◽  
Jens-Dominik Müller
Keyword(s):  
Linear Systems ◽  
Linear Models ◽  
Numerical Models ◽  
Correction Term ◽  
Industrial Test ◽  
Linear Solvers ◽  
Algorithmic Differentiation ◽  
Reverse Mode ◽  
Non Linear ◽  
Iterative Linear Solvers

Abstract Algorithmic differentiation (AD) is a widely-used approach to compute derivatives of numerical models. Many numerical models include an iterative process to solve non-linear systems of equations. To improve efficiency and numerical stability, AD is typically not applied to the linear solvers. Instead, the differentiated linear solver call is replaced with hand-produced derivative code that exploits the linearity of the original call. In practice, the iterative linear solvers are often stopped prematurely to recompute the linearisation of the non-linear outer loop. We show that in the reverse-mode of AD, the derivatives obtained with partial convergence become inconsistent with the original and the tangent-linear models, resulting in inaccurate adjoints. We present a correction term that restores consistency between adjoint and tangent-linear gradients if linear systems are only partially converged. We prove the consistency of this correction term and show in numerical experiments that the accuracy of adjoint gradients of an incompressible flow solver applied to an industrial test case is restored when the correction term is used.

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