We consider the Algorithmic Differentiation (also know as Automatic Differentiation; AD) of numerical simulation programs that contain calls to direct solvers for systems of n linear equations. AD of the linear solvers yields a local overhead of O(n) for the computation of directional derivatives or adjoints of the solution vector with respect to the system matrix and right-hand side. The local...

The role of the second order adjoint in targeting strategies is studied and analyzed. Most targeting strategies use the first order adjoint to identify regions where additional information is of potential benefit to a data assimilation system. The first order adjoint posses a restriction on the targeting time for which the linear approximation accurately tracks the evolution of perturbation. Us...

In this paper we explore two sets of polynomials, the orthogonal polynomi-als and the residual polynomials, associated with a preconditioned conjugate gradient iteration for the solution of the linear system Ax = b. In the context of preconditioning by the matrix C, we show that the roots of the orthogonal polynomials, also known as generalized Ritz values, are the eigenvalues of an orthogonal ...