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Total positivity and accurate computations with Gram matrices of Bernstein bases
In this paper, an accurate method to construct the bidiagonal factorization of Gram (mass) matrices of Bernstein bases of positive and negative...
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Improving model choice in classification: an approach based on clustering of covariance matrices
This work introduces a refinement of the Parsimonious Model for fitting a Gaussian Mixture. The improvement is based on the consideration of clusters...
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Singular value decomposition for complex matrices using two-sided Jacobi method
The two-sided Jacobi method for singular value decomposition (SVD) has the advantage of obtaining singular vectors quickly and accurately. In...
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Sparse-Aware CARM: Rooflining Locality of Sparse Computations
Sparse computation is a centre focus of modern high performance computing research. However, the complexity associated with the variety of...
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uLog: a software-based approximate logarithmic number system for computations on SIMD processors
This paper presents a new number representation based on logarithmic number system (LNS) called unsigned logarithmic number system ( ulog ), as an...
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Two party key exchange protocol based on duo circulant matrices for the IoT environment
This paper proposes a new two-party key exchange protocol based on the max-plus semiring, which is the set of matrices over the set of integers along...
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Dedicated hardware design for efficient quantum computations using classical logic gates
This work presents a novel approach to quantum computing by proposing a customizable hardware design of a dedicated processor that emulates the...
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Orthogonal Cauchy-like matrices
Cauchy-like matrices arise often as building blocks in decomposition formulas and fast algorithms for various displacement-structured matrices. A...
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BLEACH: Cleaning Errors in Discrete Computations Over CKKS
Approximated homomorphic encryption (HE) schemes such as CKKS are commonly used to perform computations over encrypted real numbers. It is commonly...
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Scalable computations for nonstationary Gaussian processes
Nonstationary Gaussian process models can capture complex spatially varying dependence structures in spatial data. However, the large number of...
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WDVV equations: symbolic computations of Hamiltonian operators
We describe software for symbolic computations that we developed in order to find Hamiltonian operators for Witten–Dijkgraaf–Verlinde–Verlinde (WDVV)...
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Development of Algorithms and Software for Modeling Controlled Dynamic Systems Using Symbolic Computations and Stochastic Methods
AbstractThe development of software for synthesizing and analyzing models of controlled systems taking into account their deterministic and...
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Authenticated key agreement scheme for IoT networks exploiting lightweight linear algebraic computations
Internet of Things (IoT) applications consist mainly of a group of small devices with sensing and/ or actuation capabilities, working collaboratively...
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Structured low-rank approximation for nonlinear matrices
Structured low-rank approximation problems are very popular in the scientific community since they are involved in several applications in different...
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Complementarity in Finite Quantum Mechanics and Computer-Aided Computations of Complementary Observables
AbstractMathematical formulation of Bohr’s complementarity principle leads to the concepts of mutually unbiased bases in Hilbert spaces and...
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Fast tridiagonalization of (p, q)-pentadiagonal matrices and its applications
( p , q )-Pentadiagonal matrices have attracted considerable attention in the past few years, which are one of the generalizations of pentadiagonal...
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QR Factorization of Block Low-Rank Matrices on Multi-instance GPU
The QR factorization, which is a fundamental operation in linear algebra, is used extensively in scientific simulations. The acceleration and memory...
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HODLR3D: hierarchical matrices for N-body problems in three dimensions
This article introduces HODLR3D, a class of hierarchical matrices arising out of N -body problems in three dimensions. HODLR3D relies on the fact that...
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Geometry-Preserving Lie Group Integrators for Differential Equations on the Manifold of Symmetric Positive Definite Matrices
In many applications, one encounters time series that lie on manifolds rather than a Euclidean space. In particular, covariance matrices are...