Related papers: Conversion Methods, Block Triangularization, and S…
In this paper, we are concerned with the problem of determining the existence of multiple equilibria in economic models. We propose a general and complete approach for identifying multiplicities of equilibria in semi-algebraic economies,…
This thesis develops numerical and theoretical approaches for understanding and analyzing singularity formation in Partial Differential Equations (PDEs). The singularity formation in the Navier-Stokes Equation (NSE) is famously challenging…
We present a code modularization approach to design efficient and massively parallel cubic and linear-scaling solvers for electronic structure calculations using atomic orbitals. The modular implementation of the orbital minimization…
Duality methods are used to generate explicit solutions to nonlinear Hodge systems, demonstrate the well-posedness of boundary value problems, and reveal, via the Hodge-B\"acklund transformation, underlying symmetries among superficially…
We propose a novel approach to tackle integrability problem for evolutionary differential-difference equations (D$\Delta$Es) on free associative algebras, also referred to as nonabelian D$\Delta$Es. This approach enables us to derive…
The generalized alternating direction method of multipliers (ADMM) of Xiao et al. [{\tt Math. Prog. Comput., 2018}] aims at the two-block linearly constrained composite convex programming problem, in which each block is in the form of…
In this paper a new block-structure method is presented for the solution of the well-known from gravity theory matrix system of equations g{ij}g{jk}=delta{i}{k} (with respect to the unknown covariant components g{ij} and by known…
We design and analyse a new numerical method to solve ODE system based on the structural method. We compute approximations of solutions together with its derivatives up to order $K$ by solving an entire block corresponding to $R$ time…
Differential-algebraic equations (DAEs) are widely used for modeling of dynamical systems. The difficulty in solving numerically a DAE is measured by its differentiation index. For highly accurate simulation of dynamical systems, it is…
In this paper, we present a new SDC scheme for solving semi-explicit DAEs with the ability to be parallelized in which only the differential equations are numerically integrated is presented. In Shu et al. (2007) it was shown that SDC for…
The exponential of block triangular matrices arises in a wide range of scientific computing applications, including exponential integrators for solving systems of ordinary differential equations, Hamiltonian systems in control theory,…
Discrete choice experiments (DCEs) investigate the attributes that influence individuals' choices when selecting among various options. To enhance the quality of the estimated choice models, researchers opt for Bayesian optimal designs that…
This paper discusses a deterministic clustering approach to capacitated resource allocation problems. In particular, the Deterministic Annealing (DA) algorithm from the data-compression literature, which bears a distinct analogy to the…
We review our recently developed electronic structure calculation methods used for the dynamics of large-scale solids or liquids with an efficient algorithm for large scale simultaneous linear equations. The electronic structure calculation…
For Kolmogorov equations associated to finite dimensional stochastic differential equations (SDEs) in high dimension, a numerical method alternative to Monte Carlo simulations is proposed. The structure of the SDE is inspired by stochastic…
This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…
In some applications there arises the need of a spatially distributed description of a physical quantity inside a device coupled to a circuit. Then, the in-space discretised system of partial differential equations is coupled to the system…
Recursive blocked algorithms have proven to be highly efficient at the numerical solution of the Sylvester matrix equation and its generalizations. In this work, we show that these algorithms extend in a seamless fashion to…
This paper addresses some numerical and theoretical aspects of dual Schur domain decomposition methods for linear first-order transient partial differential equations. In this work, we consider the trapezoidal family of schemes for…
The numerical optimization of continuous functions is a fundamental task in many scientific and engineering domains, ranging from mechanical design to training of artificial intelligence models. Among the most effective and widely used…