Related papers: A numerical method for computing the Jordan Canoni…
In this paper we present a pure algebraic construction of the normal factorization of multimode squeezed states and calculate their inner products. This procedure allows one to orthonormalize bases generated by squeezed states. We calculate…
Matrix decompositions are fundamental tools in the area of applied mathematics, statistical computing, and machine learning. In particular, low-rank matrix decompositions are vital, and widely used for data analysis, dimensionality…
The problem of approximate joint diagonalization of a collection of matrices arises in a number of diverse engineering and signal processing problems. This problem is usually cast as an optimization problem, and it is the main goal of this…
Most elementary numerical schemes found useful for solving classical trajectory problems are {\it canonical transformations}. This fact should be make more widely known among teachers of computational physics and Hamiltonian mechanics. From…
This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer method based on (rational) Krylov subspace methods for…
We present a generalisation of the pseudoinverse operation to pairs of matrices, as opposed to single matrices alone. We note the fact that the Singular Value Decomposition can be used to compute the ordinary Moore-Penrose pseudoinverse. We…
We propose a numerical method to solve the Monge-Ampere equation which admits a classical convex solution. The Monge-Ampere equation is reformulated into an equivalent first-order system. We adopt a novel reconstructed discontinuous…
This work introduces a Hamiltonian approach to regularization and linearization of central-force particle dynamics through a new canonical extension of the so-called "projective decomposition". The regularization scheme is formulated within…
In this paper, we present a determinist Jordan normal form algorithms based on the Fadeev formula: \[(\lambda \cdot I-A) \cdot B(\lambda)=P(\lambda) \cdot I\] where $B(\lambda)$ is $(\lambda \cdot I-A)$'s comatrix and $P(\lambda)$ is $A$'s…
We present in detail two resummation methods emerging from the application of the Simplified Differential Equations approach to a canonical basis of master integrals. The first one is a method which allows for an easy determination of the…
One popular way to compute the CANDECOMP/PARAFAC (CP) decomposition of a tensor is to transform the problem into a sequence of overdetermined least squares subproblems with Khatri-Rao product (KRP) structure involving factor matrices. In…
This paper presents a novel factorization-based, low-rank regularization method for solving multidimensional deconvolution problems in the frequency domain. In this approach, each frequency component of the unknown wavefield is represented…
In this paper, we focus on computing the kernel of a map of polynomial rings $\varphi$. This core problem in symbolic computation is known as implicitization. While there are extremely effective Gr\"obner basis methods used to solve this…
Large statically indeterminate truss and frame structures exhibit complex load-bearing behavior, and redundancy matrices are helpful for their analysis and design. Depending on the task, the full redundancy matrix or only its diagonal…
This work proposes a higher-order iterative framework for solving matrix equations, inspired by the structure and functionality of neural networks. A modification of the classical Jacobi iterative method is introduced to compute…
The discrimination of any pair of unknown quantum states is performed by devices processing three parts of inputs: copies of the pair of unknown states we want to discriminate are respectively stored in two program systems and copies of…
Differential equations are one of the main approaches to evaluate multi-loop Feynman integrals. The construction of a canonical or $\varepsilon$-factorised basis for multi-loop integrals remains a key bottleneck for this approach,…
Quantum computing and modern tensor-based computing have a strong connection, which is especially demonstrated by simulating quantum computations with tensor networks. The other direction is less studied: quantum computing is not often…
We exhibit an explicit, deterministic algorithm for finding a canonical form for a positive definite matrix under unimodular integral transformations. We use characteristic sets of short vectors and partition-backtracking graph software.…
This paper surveys randomized algorithms in numerical linear algebra for low-rank decompositions of matrices and tensors. The survey begins with a review of classical matrix algorithms that can be accelerated by randomized dimensionality…