Foundational optimization algorithms are the core driving force behind deep learning, evolving from early stochastic gradient descent (SGD) to the widely adopted Adam family. However, as the scale of ...

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Abstract: Bi-conjugate Gradient Method (BCG) has potential problems on slow convergence or divergence when complex linear equations are large-scale or coefficient matrix of complex linear equations is ...

Abstract: The Gauss-Seidel preconditioned conjugate gradient method applying to element-by-element finite-element method (EBE-FEM) is derived and the calculation process is presented in this paper.

Least-squares reverse-time migration (LSRTM) can overcome the problems of low resolution and unbalanced amplitude energy of deep formation imaging in reverse-time migration (RTM); hence, it can obtain ...

tree-math makes it easy to implement numerical algorithms that work on JAX pytrees, such as iterative methods for optimization and equation solving. It does so by providing a wrapper class ...

A gradient preconditioning approach based on transmitted wave energy for least-squares reverse time migration (LSRTM) is proposed in this study. The gradient is preconditioned by using the energy of ...

A convolutional neural network (CNN) with residual connections was used to train a preconditioning operator. Training and validation data were simulated using 50% brain images and 50% white Gaussian ...

In this paper, we provide and analyze a new scaled conjugate gradient method and its performance, based on the modified secant equation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method and on a ...