Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Newton's Method for Large Bound-Constrained Optimization Problems
SIAM Journal on Optimization
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Automatic Differentiation: Applications, Theory, and Implementations (Lecture Notes in Computational Science and Engineering)
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation
Advances in Automatic Differentiation
Advances in Automatic Differentiation
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
Estimating Computational Noise
SIAM Journal on Scientific Computing
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We employ recent work on computational noise to obtain near-optimal difference estimates of the derivative of a noisy function. Our analysis relies on a stochastic model of the noise without assuming a specific form of distribution. We use this model to derive theoretical bounds for the errors in the difference estimates and obtain an easily computable difference parameter that is provably near-optimal. Numerical results closely resemble the theory and show that we obtain accurate derivative estimates even when the noisy function is deterministic.