Related papers: A modified Newmark/Newton-Raphson method with auto…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
This article generalizes a recently introduced procedure to solve nonlinear systems of equations, radically departing from the conventional Newton-Raphson scheme. The original nonlinear system is first unfolded into three simpler…
Von Neumann stability analysis, a well-known Fourier-based method, is a widely used technique for assessing stability in numerical computations. However, as noted in "Numerical Solution of Partial Differential Equations: Finite Difference…
Neural radiance fields (NeRFs) have gained popularity in the autonomous driving (AD) community. Recent methods show NeRFs' potential for closed-loop simulation, enabling testing of AD systems, and as an advanced training data augmentation…
Neutron reflectometry (NR) is a powerful technique to probe surfaces and interfaces. NR is inherently an indirect measurement technique, access to the physical quantities of interest (layer thickness, scattering length density, roughness),…
Integro-differential equations arise in a wide range of applications, including transport, kinetic theory, radiative transfer, and multiphysics modeling, where nonlocal integral operators couple the solution across phase space. Such…
We study the use of feedforward neural networks (FNN) to develop models of nonlinear dynamical systems from data. Emphasis is placed on predictions at long times, with limited data availability. Inspired by global stability analysis, and…
In this paper we develop convergence and acceleration theory for Anderson acceleration applied to Newton's method for nonlinear systems in which the Jacobian is singular at a solution. For these problems, the standard Newton algorithm…
Randomized iterative methods have gained recent interest in machine learning and signal processing for solving large-scale linear systems. One such example is the randomized Douglas-Rachford (RDR) method, which updates the iterate by…
In detailled buiding simulation models, airflow modelling and solving are still open and crucial problems, specially in the case of open buildings as encountered in tropical climates. As a consequence, wind speed conditioning indoor thermal…
The successes of deep learning, variational inference, and many other fields have been aided by specialized implementations of reverse-mode automatic differentiation (AD) to compute gradients of mega-dimensional objectives. The AD…
In this paper, a novel multigrid method based on Newton iteration is proposed to solve nonlinear eigenvalue problems. Instead of handling the eigenvalue $\lambda$ and eigenfunction $u$ separately, we treat the eigenpair $(\lambda, u)$ as…
The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. We show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix…
In this work we describe an Adaptive Regularization using Cubics (ARC) method for large-scale nonconvex unconstrained optimization using Limited-memory Quasi-Newton (LQN) matrices. ARC methods are a relatively new family of optimization…
Transformers and linear state space models can be evaluated in parallel on modern hardware, but evaluating nonlinear RNNs appears to be an inherently sequential problem. Recently, however, Lim et al. '24 developed an approach called DEER,…
In this paper, we develop a variant of the well-known Gauss-Newton (GN) method to solve a class of nonconvex optimization problems involving low-rank matrix variables. As opposed to the standard GN method, our algorithm allows one to handle…
The focus in this work is on interior-point methods for inequality-constrained quadratic programs, and particularly on the system of nonlinear equations to be solved for each value of the barrier parameter. Newton iterations give high…
Machine learning and neural network models in particular have been improving the state of the art performance on many artificial intelligence related tasks. Neural network models are typically implemented using frameworks that perform…
We develop nested automatic differentiation (AD) algorithms for exact inference and learning in integer latent variable models. Recently, Winner, Sujono, and Sheldon showed how to reduce marginalization in a class of integer latent variable…
In finance, implied volatility is an important indicator that reflects the market situation immediately. Many practitioners estimate volatility using iteration methods, such as the Newton--Raphson (NR) method. However, if numerous implied…