Related papers: Algorithms for Recursive Block Matrices
We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed…
We showcase applications of nonlinear algebra in the sciences and engineering. Our review is organized into eight themes: polynomial optimization, partial differential equations, algebraic statistics, integrable systems, configuration…
We study the problem of computing the matrix exponential of a block triangular matrix in a peculiar way: Block column by block column, from left to right. The need for such an evaluation scheme arises naturally in the context of option…
In some matrix formations, factorizations and transformations, we need special matrices with some properties and we wish that such matrices should be easily and simply generated and of integers. In this paper, we propose a zero-sum rule for…
The purpose of this paper is to make the theory of vertex algebras trivial. We do this by setting up some categorical machinery so that vertex algebras are just ``singular commutative rings'' in a certain category. This makes it easy to…
In this paper we classify, up to isomorphism, the superinvolutions on algebras of upper block-triangular matrices over an algebraically closed field of characteristic different from $2$.
Using the language of Riordan arrays, we look at two related iterative processes on matrices and determine which matrices are invariant under these processes. In a special case, the invariant sequences that arise are conjectured to have…
We introduce an extension of the Difference of Convex Algorithm (DCA) in the form of a randomized block coordinate approach for problems with separable structure. For $n$ coordinate-blocks and $k$ iterations, our main result proves a…
Using simultaneously two operator identities, we consider the inversion of the convolution operators on a rectangular. The structure of the inverse operators and of some corresponding forms, which are important in signal processing, is…
We construct two bases for each cluster algebra coming from a triangulated surface without punctures. We work in the context of a coefficient system coming from a full-rank exchange matrix, for example, principal coefficients.
A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination…
In this article, we revisit some block matrix construction methods and use them to derive various general expansion formulas for calculating the ranks of matrix expressions. As applications, we derive a variety of interesting rank…
A g-circulant matrix of order n is defined as a matrix of order n where each row is a right cyclic shift in g-places to the preceding row. Using number theory, certain nonnegative g-circulant real matrices are constructed. In particular, it…
The matrix inversion is an interesting topic in algebra mathematics. However, to determine an inverse matrix from a given matrix is required many computation tools and time resource if the size of matrix is huge. In this paper, we have…
We show that in the presence of random Kripke's schema choice sequences can be recursively encoded in intuitionistic real algebra.
We introduce the concept of reflexive moment functional in two variables and the definition of reflexive orthogonal polynomial system. Also reverse matrices and their interesting algebraic properties are studied. Reverse matrices and…
A Maple implementation of partitioned matrices is described. A recursive block data structure is used, with all operations preserving the block abstraction. These include constructor functions, ring operations such as addition and product,…
Matrix inversion problems are often encountered in experimental physics, and in particular in high-energy particle physics, under the name of unfolding. The true spectrum of a physical quantity is deformed by the presence of a detector,…
We derive an algorithm for mutating quivers of 2-CY tilted algebras that have loops and 2-cycles, under certain specific conditions. Further, we give the classification of the 2-CY tilted algebras coming from standard algebraic 2-CY…
We introduce matrix and its block to the Dung's theory of argumentation framework. It is showed that each argumentation framework has a matrix representation, and the indirect attack relation and indirect defence relation can be…