Related papers: Solving the 3x3 Real Symmetric Eigenproblem
Until now, Computer Scientists have concerned themselves with identifying efficient algorithms for solving the general case of some problem -- that is finding one which performs well when the size of the input tends to infinity. In this…
This paper proposes a combination of a hybrid CPU--GPU and a pure GPU software implementation of a direct algorithm for solving shifted linear systems $(A - \sigma I)X = B$ with large number of complex shifts $\sigma$ and multiple…
The problem of solving a system of polynomial equations is one of the most fundamental problems in applied mathematics. Among them, the problem of solving a system of binomial equations form a important subclass for which specialized…
We present a fully grid-based approach for solving Hartree-Fock and all-electron Kohn-Sham equations based on low-rank approximation of three-dimensional electron orbitals. Due to the low-rank structure the total complexity of the algorithm…
We propose a new hybrid topology optimization algorithm based on multigrid approach that combines the parallelization strategy of CPU using OpenMP and heavily multithreading capabilities of modern Graphics Processing Units (GPU). In…
Solving eigenproblem of the Laplacian matrix of a fully connected weighted graph has wide applications in data science, machine learning, and image processing, etc. However, this is very challenging because it involves expensive matrix…
A one-sided Jacobi hyperbolic singular value decomposition (HSVD) algorithm, using a massively parallel graphics processing unit (GPU), is developed. The algorithm also serves as the final stage of solving a symmetric indefinite eigenvalue…
The 3D mesh is an important representation of geometric data. In the generation of mesh data, geometric deficiencies (e.g., duplicate elements, degenerate faces, isolated vertices, self-intersection, and inner faces) are unavoidable and may…
The Hidden Subgroup Problem is used in many quantum algorithms such as Simon's algorithm and Shor's factoring and discrete log algorithms. A polynomial time solution is known in case of abelian groups, and normal subgroups of arbitrary…
We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract…
We study the problem of deleting a minimum cost set of vertices from a given vertex-weighted graph in such a way that the resulting graph has no induced path on three vertices. This problem is often called cluster vertex deletion in the…
This paper proposes a new algorithm for simultaneous graph matching and clustering. For the first time in the literature, these two problems are solved jointly and synergetically without relying on any training data, which brings advantages…
We present efficient implementations of atom reconfiguration algorithms for both CPUs and GPUs, along with a batching routine to merge displacement operations for parallel execution. Leveraging graph-theoretic methods, our approach derives…
This thesis studies the graph alignment problem, the noisy version of the graph isomorphism problem, which aims to find a matching between the nodes of two graphs which preserves most of the edges. Focusing on the planted version where the…
We formulate and analyze a goal-oriented adaptive finite element method for a symmetric linear elliptic partial differential equation (PDE) that can simultaneously deal with multiple linear goal functionals. In each step of the algorithm,…
This paper introduces JAX-FEM, an open-source differentiable finite element method (FEM) library. Constructed on top of Google JAX, a rising machine learning library focusing on high-performance numerical computing, JAX-FEM is implemented…
In this paper, we propose new algorithms for finding a common point of the solution set of a pseudomonotone equilibrium problem and the set of fixed points of a symmetric generalized hybrid mapping in a real Hilbert space. The convergence…
Finite element methods for electromagnetic problems modeled by Maxwell-type equations are highly sensitive to the conformity of approximation spaces, and non-conforming methods may cause loss of convergence. This fact leads to an essential…
With the regular decomposition technique, we decompose the space $\mathbf{H}_0^s(\mathbf{curl}; \Omega)$ into the sum of a vector potential space and the gradient of a scalar space, both possessing higher regularity. Based on this new high…
In this paper, mathematical models for cuff-tissue-artery system are developed and simplified into an axisymmetric problem in space. It is nonlinear properties of cuff and artery wall that make it difficult to solve elastic equations…