Related papers: A tensorial-parallel Chebyshev method for a differ…
This work is concerned with linear matrix equations that arise from the space-time discretization of time-dependent linear partial differential equations (PDEs). Such matrix equations have been considered, for example, in the context of…
In one of the most important methods in Density Functional Theory - the Full-Potential Linearized Augmented Plane Wave (FLAPW) method - dense generalized eigenproblems are organized in long sequences. Moreover each eigenproblem is strongly…
The PC algorithm is the state-of-the-art algorithm for causal structure discovery on observational data. It can be computationally expensive in the worst case due to the conditional independence tests are performed in an…
Cholesky factorization is a widely used method for solving linear systems involving symmetric, positive-definite matrices, and can be an attractive choice in applications where a high degree of numerical stability is needed. One such…
In this work, we study the distributed Nash equilibrium seeking problem for monotone generalized noncooperative games with set constraints and shared affine inequality constraints. A distributed regularized penalty method is proposed. The…
The focus of my PhD thesis is on exploring parallel approaches to efficiently solve problems modeled by constraints and presenting a new proposal. Current solvers are very advanced; they are carefully designed to effectively manage the…
In this dissertation, we analyze the computational properties of game-theoretic centrality measures. The key idea behind game-theoretic approach to network analysis is to treat nodes as players in a cooperative game, where the value of each…
This paper presents a novel parallel-in-time algorithm able to compute time-periodic solutions of problems where the period is not given. Exploiting the idea of the multiple shooting method, the proposed approach calculates the initial…
Together with the improvements in state-of-the-art accuracies of various tasks, deep learning models are getting significantly larger. However, it is extremely difficult to implement these large models because limited GPU memory makes it…
Reservoir computers can be used to predict time series generated by spatio-temporal chaotic systems. Using multiple reservoirs in parallel has shown improved performances for these predictions, by effectively reducing the input…
A fast multilevel algorithm based on directionally scaled tensor-product Gaussian kernels on structured sparse grids is proposed for interpolation of high-dimensional functions and for the numerical integration of high-dimensional…
We present efficient and scalable parallel algorithms for performing mathematical operations for low-rank tensors represented in the tensor train (TT) format. We consider algorithms for addition, elementwise multiplication, computing norms…
The Prisoner's Dilemma game has a long history stretching across the social, biological, and physical sciences. In 2012, Press and Dyson developed a method for analyzing the mapping of the 8-dimensional strategy profile onto the…
For a function that is analytic on and around an interval, Chebyshev polynomial interpolation provides spectral convergence. However, if the function has a singularity close to the interval, the rate of convergence is near one. In these…
Saddle point with a given Morse index on a potential energy surface is an important object related to energy landscape in physics and chemistry. Efficient numerical methods based on iterative minimization formulation have been proposed in…
Matrix diagonalization is almost always involved in computing the density matrix needed in quantum chemistry calculations. In the case of modest matrix sizes ($\lesssim$ 5000), performance of traditional dense diagonalization algorithms on…
Optimal multiple sequence alignment by dynamic programming, like many highly dimensional scientific computing problems, has failed to benefit from the improvements in computing performance brought about by multi-processor systems, due to…
A geometric approach to differential game theory is illustrated. The parallel pursuit is considered as a two-player zero-sum differential game. The optimal strategies of each player is designed based on Riemann-Finsler geometry. Our…
Continuous and discrete game-theoretic models of dispersed material drying process are formalized and studied in the paper. The existence of optimal drying strategies is shown through application of results from the theory of differential…
Solving inverse problems and achieving statistical rigour in landscape evolution models requires running many model realizations. Parallel computation is necessary to achieve this in a reasonable time. However, no previous algorithm is…