Related papers: The LAPW method with eigendecomposition based on t…
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…
Coupled decompositions are a widely used tool for data fusion. As the volume of data increases, so does the dimensionality of matrices and tensors, highlighting the need for more efficient coupled decomposition algorithms. This paper…
The computation of a few singular triplets of large, sparse matrices is a challenging task, especially when the smallest magnitude singular values are needed in high accuracy. Most recent efforts try to address this problem through…
We present a method for the fast computation of the eigenpairs of a bijective positive symmetric linear operator $\mathcal{L}$. The method is based on a combination of operator adapted wavelets (gamblets) with hierarchical subspace…
We study the eigendecompositions of para-Hermitian matrices $H(z)$, that is, matrix-valued functions that are analytic and Hermitian on the unit circle $S^1 \subset \mathbb C$. In particular, we fill existing gaps in the literature and…
Let $\varphi:\mathbb D \to \mathbb D$ be a parabolic self-map of the unit disc $\mathbb D$ having zero hyperbolic step. We study holomorphic self-maps of $\mathbb D$ commuting with $\varphi$. In particular, we answer a question from Gentili…
We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization…
We present a hybrid numerical approach to simulate quantum many body problems on two spatial dimensional quantum lattice models via the non-Abelian ab initio version of the density matrix renormalization group method on state-of-the-art…
We present a matrix-free parallel scalable multilevel deflation preconditioned method for heterogeneous time-harmonic wave problems. Building on the higher-order deflation preconditioning proposed by Dwarka and Vuik (SIAM J. Sci. Comput.…
Singular value decomposition is widely used in modal analysis, such as proper orthogonal decomposition and resolvent analysis, to extract key features from complex problems. SVD derivatives need to be computed efficiently to enable the…
A novel parallel algorithm for matrix multiplication is presented. The hyper-systolic algorithm makes use of a one-dimensional processor abstraction. The procedure can be implemented on all types of parallel systems. It can handle…
Learning a dynamical system from input/output data is a fundamental task in the control design pipeline. In the partially observed setting there are two components to identification: parameter estimation to learn the Markov parameters, and…
Let F be a non Archimedean locally compact field of residue characteristic different from 2, let G be a connected reductive group defined over F, let s be an involutive F-automorphism of G and H an open F-subgroup of the fixed points group…
The hierarchical matrix framework partitions matrices into subblocks that are either small or of low numerical rank, enabling linear storage complexity and efficient matrix-vector multiplication. This work focuses on the $H^2$-matrix format…
This paper proposes a homogeneous second-order descent framework (HSODF) for nonconvex and convex optimization based on the generalized homogeneous model (GHM). In comparison to the Newton steps, the GHM can be solved by extremal symmetric…
The main purpose of this paper is to compute all irreducible spherical functions on $G={SL}(2,{\mathbb C})$ of arbitrary type $\delta\in \hat K$, where $K={SU}(2)$. This is accomplished by associating to a spherical function $\Phi$ on $G$ a…
The joint bidiagonalization (JBD) process of a regular matrix pair $\{A,L\}$ is mathematically equivalent to two simultaneous Lanczos bidiagonalization processes of the upper and lower parts of the Q-factor of QR factorization of the…
In this work we describe an efficient implementation of a hierarchy of algorithms for the decomposition of dense matrices over the field with two elements (GF(2)). Matrix decomposition is an essential building block for solving dense…
We examine the properties and consequences of pseudo-supersymmetry for quantum systems admitting a pseudo-Hermitian Hamiltonian. We explore the Witten index of pseudo-supersymmetry and show that every pair of diagonalizable (not necessarily…
In this paper we present an improved dqds algorithm for computing all the singular values of a bidiagonal matrix to high relative accuracy. There are two key contributions: a novel deflation strategy that improves the convergence for badly…