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A numerical differentiation library exploiting parallel architectures
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DOI：10.1016/j.cpc.2009.02.004.png)
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Abstract
En 中文
We present a software library for numerically estimating first and second order partial derivatives of a function by finite differencing. Various truncation schemes are offered resulting in corresponding formulas that are accurate to order O(h), O(h(2)), and O(h(4)), h being the differencing step. The derivatives are calculated via forward, backward and central differences. Care has been taken that only feasible points are used in the case where bound constraints are imposed on the variables. The Hessian may be approximated either from function or from gradient values. There are three versions of the software: a sequential version, an OpenMP version for shared memory architectures and an MPI version for distributed systems (clusters). The parallel versions exploit the multiprocessing capability offered by computer clusters, as well as modern multi-core systems and due to the independent character of the derivative computation, the speedup scales almost linearly with the number of available processors/cores.
Keywords:
Numerical differentiation
Finite differences
Optimization
Nonlinear equations
OpenMP
MPI
Parallel processing
Distributed computing
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