Advancements in Algorithmic Differentiation and Formal Verification

The field is witnessing a significant shift towards enhancing the efficiency and precision of algorithmic differentiation tools, with a particular focus on mixed-precision methods and the incorporation of complex numbers. This movement is driven by the need for faster and more accurate computations in various applications, including linear systems solvers and matrix-matrix multiplications. Furthermore, advancements in formal verification are being made, with the development of new features and techniques that support the implementation of floating-point operations and mutable objects. Noteworthy papers include: Towards a mixed-precision ADI method for Lyapunov equations, which demonstrates the potential of mixed-precision methods for certain applications. Adding complex numbers to expression template algorithmic differentiation tools, which highlights the benefits of integrating complex number operations into modern operator overloading AD tools.

Sources

Extended Abstract: Partial-encapsulate and Its Support for Floating-point Operations in ACL2

Extended Abstract: Mutable Objects with Several Implementations

Towards a mixed-precision ADI method for Lyapunov equations

Adding complex numbers to expression template algorithmic differentiation tools

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