Related papers: Reduced normal form of local integral bases

We present generic expressions for the integrands of canonical bases under maximal cut in elliptic Feynman integral families with multiple kinematic scales. Such integrals frequently arise in phenomenologically relevant scattering…

Spherical functions appear throughout computer graphics, from spherical harmonic lighting and precomputed radiance transfer to neural radiance fields and procedural planet rendering. Efficient evaluation is critical for real-time…

We consider the computation of two normal forms for matrices over the univariate polynomials: the Popov form and the Hermite form. For matrices which are square and nonsingular, deterministic algorithms with satisfactory cost bounds are…

Computing homology and cohomology is at the heart of many recent works and a key issue for topological data analysis. Among homological objects, homology generators are useful to locate or understand holes (especially for geometric…

In this paper, a polynomial-time algorithm is given to compute the generalized Hermite normal form for a matrix F over Z[x], or equivalently, the reduced Groebner basis of the Z[x]-module generated by the column vectors of F. The algorithm…

This paper offers a review of numerical methods for computation of the eigenvalues of Hermitian matrices and the singular values of general and some classes of structured matrices. The focus is on the main principles behind the methods that…

An algorithm to classify a general Hermitian matrix according to its signature (positive semi-definite, negative or indefinite) is presented. It builds on the Quantum Phase Estimation algorithm, which stores the sign of the eigenvalues of a…

This paper proposes SAT-based techniques to calculate a specific normal form of a given finite mathematical structure (model). The normal form is obtained by permuting the domain elements so that the representation of the structure is…

In this contribution, we introduce and numerically evaluate a certified and adaptive localized reduced basis method as a local model in a trust-region optimization method for parameter optimization constrained by partial differential…

We study some properties of quadratic forms with values in a field whose underlying vector spaces are endowed with the structure of right vector spaces over a division ring extension of that field. Some generalized notions of isotropy,…

Partial differential equations can be used to model many problems in several fields of application including, e.g., fluid mechanics, heat and mass transfer, and electromagnetism. Accurate discretization methods (e.g., finite element or…

A Las Vegas randomized algorithm is given to compute the Hermite normal form of a nonsingular integer matrix $A$ of dimension $n$. The algorithm uses quadratic integer multiplication and cubic matrix multiplication and has running time…

In these lectures we give an introduction to the reduction theory of binary forms starting with quadratic forms with real coefficients, Hermitian forms, and then define the Julia quadratic for any degree $n$ binary form. A survey of a…

The Reduced Basis Method (RBM) is a model reduction technique used to solve parametric PDEs that relies upon a basis set of solutions to the PDE at specific parameter values. To generate this reduced basis, the set of a small number of…

We give a number of constructions where inverse limits seriously degrade properties of regular rings, such as unit-regularity, diagonalisation of matrices, and finite stable rank. This raises the possibility of using inverse limits to…

Dirichlet integrals and the associated Dirichlet statistical densities are widely used in various areas. Generalizations of Dirichlet integrals and Dirichlet models to matrix-variate cases, when the matrices are real symmetric positive…

We present an algorithm for computing a Smith form with multipliers of a regular matrix polynomial over a field. This algorithm differs from previous ones in that it computes a local Smith form for each irreducible factor in the determinant…

Following arXiv:2303.02992, we develop an approach to the Hamiltonian theory of normal forms based on continuous averaging. We concentrate on the case of normal forms near an elliptic singular point, but unlike arXiv:2303.02992 we do not…

Reduced order models are computationally inexpensive approximations that capture the important dynamical characteristics of large, high-fidelity computer models of physical systems. This paper applies machine learning techniques to improve…

In this paper we adapt the method of [P. H. Baptistelli, M. Manoel and I. O. Zeli. Normal form theory for reversible equivariant vector fields. Bull. Braz. Math. Soc., New Series 47 (2016), no. 3, 935-954] to obtain normal forms of a class…