相关论文: Convergence improvement for coupled cluster calcul…
It is shown that the problem of balancing a nonnegative matrix by positive diagonal matrices can be recast as a constrained nonlinear multiparameter eigenvalue problem. Based on this equivalent formulation some adaptations of the power…
We propose fork-join and task-based hybrid implementations of four classical linear algebra iterative methods (Jacobi, Gauss-Seidel, conjugate gradient and biconjugate gradient stabilised) as well as variations of them. Algorithms are duly…
We consider a multi-block separable convex optimization problem with the linear constraints, where the objective function is the sum of m individual convex functions without overlapping variables. The linearized version of the generalized…
Block matrix structure is commonly arising is various physics and engineering applications. There are various advantages in preserving the blocks structure while computing the inversion of such partitioned matrices. In this context, using…
A known first order method to find a feasible solution to a conic problem is an adapted von Neumann algorithm. We improve the distance reduction step there by projecting onto the convex hull of previously generated points using a primal…
In one dimensional transport problems the scattering matrix $S$ is decomposed into a block structure corresponding to reflection and transmission matrices at the two ends. For $S$ a random unitary matrix, the singular value probability…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
This note shows how to compute, to high relative accuracy under mild assumptions, complex Jacobi rotations for diagonalization of Hermitian matrices of order two, using the correctly rounded functions $\mathtt{cr\_hypot}$ and…
Iterative methods for solving large sparse systems of linear equations are widely used in many HPC applications. Extreme scaling of these methods can be difficult, however, since global communication to form dot products is typically…
The new class of alternating-conjugate splitting methods is presented and analyzed. They are obtained by concatenating a given composition involving complex coefficients with the same composition but with the complex conjugate coefficients.…
A real vector space combined with an inverse for vectors is sufficient to define a vector continued fraction whose parameters consist of vector shifts and changes of scale. The choice of sign for different components of the vector inverse…
The primal-dual interior point method (IPM) is widely regarded as the most efficient IPM variant for linear optimization. In this paper, we demonstrate that the improved stability of the pure primal IPM can allow speedups relative to a…
The Frank Wolfe algorithm (FW) is a popular projection-free alternative for solving large-scale constrained optimization problems. However, the FW algorithm suffers from a sublinear convergence rate when minimizing a smooth convex function…
This paper reviews recent results on hybrid inverse problems, which are also called coupled-physics inverse problems of multi-wave inverse problems. Inverse problems tend to be most useful in, e.g., medical and geophysical imaging, when…
We study iteration maps of recurrence relations arising from mutation periodic quivers of arbitrary period. Combining tools from cluster algebra theory and (pre)symplectic geometry, we show that these cluster iteration maps can be reduced…
With the development of machine learning and Big Data, the concepts of linear and non-linear optimization techniques are becoming increasingly valuable for many quantitative disciplines. Problems of that nature are typically solved using…
Most dimensionality reduction methods employ frequency domain representations obtained from matrix diagonalization and may not be efficient for large datasets with relatively high intrinsic dimensions. To address this challenge, Correlated…
We find that imposing the crossing symmetry in the iteration process considerably extends the range of convergence for solutions of the parquet equations for the Hubbard model. When the crossing symmetry is not imposed, the convergence of…
Multilevel methods represent a powerful approach in numerical solution of partial differential equations. The multilevel structure can also be used to construct estimates for total and algebraic errors of computed approximations. This paper…
Dual quaternion matrices have various applications in robotic research and its spectral theory has been extensively studied in recent years. In this paper, we extend Jacobi method to compute all eigenpairs of dual quaternion Hermitian…