Related papers: Block-diagonalisation of matrices and operators
The decomposition method which makes the parallel solution of the block-tridiagonal matrix systems possible is presented. The performance of the method is analytically estimated based on the number of elementary multiplicative operations…
Bernstein polynomials, long a staple of approximation theory and computational geometry, have also increasingly become of interest in finite element methods. Many fundamental problems in interpolation and approximation give rise to…
Various quantum algorithms require usage of arbitrary diagonal operators as subroutines. For their execution on a physical hardware, those operators must be first decomposed into target device's native gateset and its qubit connectivity for…
The motivation of this paper is twofold. First, we investigate the block-diagonalization of the $z$-block circulant matrix $\mathtt{bcirc_z}(\mathcal A)$, based on this block-diagonal structure, and develop the algorithm…
We describe the graded isomorphisms of rings of endomorphisms of graded flags over graded division algebras. As a consequence describe the isomorphism classes of upper block triangular matrix algebras (over an algebraically closed field of…
Randomized sampling has recently been demonstrated to be an efficient technique for computing approximate low-rank factorizations of matrices for which fast methods for computing matrix vector products are available. This paper describes an…
In this article we extend the adaptive cross approximation (ACA) method known for the efficient approximation of discretisations of integral operators to a block-adaptive version. While ACA is usually employed to assemble hierarchical…
Simultaneous matrix diagonalization is used as a subroutine in many machine learning problems, including blind source separation and paramater estimation in latent variable models. Here, we extend algorithms for performing joint…
In this paper we consider disjoint decomposition of algebraic and non-linear partial differential systems of equations and inequations into so-called simple subsystems. We exploit Thomas decomposition ideas and develop them into a new…
The cost of data input can dominate the run-time of quantum algorithms. Here, we consider data input of arithmetically structured matrices via block encoding circuits, the input model for the quantum singular value transform and related…
We establish an algorithm for a criterion of the diagonalisability of a matrix over a local field by a unitary matrix. For this sake, we define the notion of normality of a $p$-adic operator, and give several criteria for the normality. We…
Using the decomposition of semimagic squares into the associated and balanced symmetry types as a motivation, we introduce an equivalent representation in terms of block-structured matrices. This block representation provides a way of…
This paper is a tutorial in a general and explicit procedure to simplify semidefinite programs which are invariant under the action of a symmetry group. The procedure is based on basic notions of representation theory of finite groups. As…
In the present paper, we propose a block variant of the extended Hessenberg process for computing approximations of matrix functions and other problems producing large-scale matrices. Applications to the computation of a matrix function…
Block encoding severs as an important data input model in quantum algorithms, enabling quantum computers to simulate non-unitary operators effectively. In this paper, we propose an efficient block-encoding protocol for sparse matrices based…
We study a family of semiample divisors on $\bar{M}_{0,n}$ defined using conformal blocks and analyze their associated morphisms.
In the theory of open quantum systems, divisibility of the system dynamical maps is related to memory effects in the dynamics. By decomposing the system Hilbert space as a direct sum of several Hilbert spaces, we study the relationship…
We construct generalized additional symmetries of a two-component BKP hierarchy defined by two pseudo-differential Lax operators. These additional symmetry flows form a Block type algebra with some modified(or additional) terms because of a…
In this paper, we will provide constructions of D-module structures on the complex computing the periodic cyclic homology of a stable infinity-category defined over a scheme of characteristic zero. We give two methods. The first one is…
This work continues the research of generalized Heisenberg algebras connected with several orthogonal polynomial systems. The realization of the annihilation operator of the algebra corresponding to a polynomial system by a differential…