Related papers: Strassen $2\times2$ Matrix Multiplication from a 3…
This article presents a new semi-automatic method for charge and mass identification in two-dimensional matrices. The proposed algorithm is based on the matrix's properties and uses as little information as possible on the global form of…
We study a $2 \times 2$ matrix equation arising naturally in the theory of Coxeter frieze patterns. It is formulated in terms of the generators of the group $\mathrm{PSL}(2,\mathbb{Z})$ and is closely related to continued fractions. It…
The N=2 supersymmetry in quantum mechanics involving two-component eigenfunction is investigated.
We design a 3/2 approximation algorithm for the Generalized Steiner Tree problem (GST) in metrics with distances 1 and 2. This is the first polynomial time approximation algorithm for a wide class of non-geometric metric GST instances with…
Distributed-memory matrix multiplication (MM) is a key element of algorithms in many domains (machine learning, quantum physics). Conventional algorithms for dense MM rely on regular/uniform data decomposition to ensure load balance. These…
Schemes for exact multiplication of small matrices have a large symmetry group. This group defines an equivalence relation on the set of multiplication schemes. There are algorithms to decide whether two schemes are equivalent. However, for…
We present a scenario for deriving Maxwell theory from IIB matrix model. Four dimensional spacetime and theories on it relate different dimensional ones by applying appropriate limits of the backgrounds of matrix model. It is understood by…
An equivalence of matrices via semi-tensor product (STP) is proposed. Using this equivalence, the quotient space is obtained. Parallel and sequential arrangements of the natural projection on different shapes of matrices leads to the…
Matrix multiplication is a fundamental classical computing operation whose efficiency becomes a major challenge at scale, especially for machine learning applications. Quantum computing, with its inherent parallelism and exponential storage…
While there are numerous linear algebra teaching tools, they tend to be focused on the basics, and not handle the more advanced aspects. This project aims to fill that gap, focusing specifically on methods like Strassen's fast matrix…
We prove a Hausdorff dimension result for the image of two-dimensional multiplicative cascade processes, and we obtain from this result a KPZ-type formula which normally has one point of phase transition.
This note gives a simple analysis of a randomized approximation scheme for matrix multiplication proposed by Sarlos (2006) based on a random rotation followed by uniform column sampling. The result follows from a matrix version of…
In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…
We study regularization of matrices in the covariant derivative interpretation of matrix models, a typical example of which is the type IIB matrix model. The covariant derivative interpretation provides a possible way in which curved…
In this paper, we study the numerical solutions of the multi-dimensional spatial fractional Allen-Cahn equations. After semi-discretization for the spatial fractional Riesz derivative, a system of nonlinear ordinary differential equations…
The study of the combinatorial diameter of a polyhedron is a classical topic in linear-programming theory due to its close connection with the possibility of a polynomial simplex-method pivot rule. The 2-sum operation is a classical…
This paper proposes new factorizations for computing the Neumann series. The factorizations are based on fast algorithms for small prime sizes series and the splitting of large sizes into several smaller ones. We propose a different basis…
The emergence of (3+1)-dimensional expanding space-time in the Lorentzian type IIB matrix model is an intriguing phenomenon which was observed in Monte Carlo studies of this model. In particular, this may be taken as a support to the…
Matrix square roots and their inverses arise frequently in machine learning, e.g., when sampling from high-dimensional Gaussians $\mathcal{N}(\mathbf 0, \mathbf K)$ or whitening a vector $\mathbf b$ against covariance matrix $\mathbf K$.…
There are many two-by-two matrices in layer optics. It is shown that they can be formulated in terms of a three-parameter group whose algebraic property is the same as the group of Lorentz transformations in a space with two space-like and…