We develop a numerically efficient algorithm for computing controls for nonlinear systems that minimize a quadratic performance measure. We formulate the optimal control problem in discrete-time, but ...

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The current state-of-the-art time series modeling architectures include Recurrent Neural Networks (RNN), ordinary differential equation (ODE) based, and flow-matching methods. They have successfully ...

In this work, we propose a new method to enhance the convergence rate of an iterative algorithm used to solve a system of equations with an arbitrary condition number. At each stage, the algorithm ...

In any case, Cornacchia’s algorithm provides a systematic way to find integer solutions to quadratic equations, exploiting the particular properties of each quadratic form.

In this paper, a new mathematical method is used to study the indefinite equations of binary quadratic and binary arbitrary order, the problem of judging and solving these indefinite equations with or ...

It is common knowledge that the future quadratic programming (FQP) problem is a challenging and widely applicable topic in mathematical science and many engineering fields. In this article, we ...

More generally, this algorithm caters to the class of elliptic and parabolic PDEs described by d-dimensional Laplace, Poisson, and heat equations. Under certain boundary conditions, the flows under ...