An efficient direct solver for volume integral equations with O(N) complexity for a broad range of problems is presented. The solver relies on hierarchical compression of the discretized integral operator, and exploits that off-diagonal blocks of certain dense matrices have numerically low rank. Technically, the solver is inspired by previously developed direct solvers for integral equations ba...

The two most successful methods of estimating the distribution of NMR relaxation times from two dimensional data are firstly a data compression stage followed by application of the Butler-Reeds-Dawson (BRD) algorithm, and secondly a primal dual interior point method using a preconditioned conjugate gradient (PCG). Both of these methods have been presented in the literature as requiring a trunca...

alzheimer’s disease (ad) is a uniquely human disorder. although the pathogenesis of ad is not fully understood, growing evidence indicates that the deposition of beta-amyloid (aβ) and the local reactions of various cell types to this protein play major roles in the development of the disease. in the present study transgenic mice expressing mutant amyloid precursor protein (app) has been used. t...

Abstract Masonry components are frequently limited to increase structural capacity. Concrete confinement models commonly used develop generalised approaches for assessing the behaviour of confined masonry columns. and masonry, on other hand, differ significantly in terms physical mechanical qualities. Recent scientific studies experimental constrained columns have supplied useful knowledge. Whe...

Abstract We introduce three developments within the stochastic many-body perturbation theory: efficient evaluation of off-diagonal self-energy terms, construction Dyson orbitals, and constrained random phase approximation. The approaches readily handle systems with thousands atoms. use them to explore electronic states twisted bilayer graphene (tBLG) characterized by giant unit cells correlated...

In this paper, based on the block (element)-wise inverse Jacket matrix, a unified fast hybrid diagonal block-wise transform (FHDBT) algorithm is proposed. A new fast diagonal block matrix decomposition is made by the matrix product of successively lower order diagonal Jacket matrix and Hadamard matrix. Using a common lower order matrix in the form of 1 1, a fast recursive structure can be devel...

We present a data structure and several operations it supports for recursively lowrank compressed matrices; that is, the diagonal blocks of the matrix are recursively partitioned, and the off-diagonal blocks in each partition level admit a low-rank approximation. Such a compression is embraced in many linearor near-linear-time methods for kernel matrices, including the fast multipole method, th...

We characterize the natural diagonal almost product (locally product) structures on the tangent bundle of a Riemannian manifold. We obtain the conditions under which the tangent bundle endowed with the determined structure and with a metric of natural diagonal lift type is a Riemannian almost product (locally product) manifold, or an (almost) para-Hermitian manifold. We find the natural diagona...

Given a symmetric positive definite matrix A, we compute a structured approximate Cholesky factorization A ≈ RTR up to any desired accuracy, where R is an upper triangular hierarchically semiseparable (HSS) matrix. The factorization is stable, robust, and efficient. The method compresses off-diagonal blocks with rank-revealing orthogonal decompositions. In the meantime, positive semidefinite te...