Search results for "Linear Algebra"
showing 10 items of 552 documents
Understanding the shortcomings of commodity-based technology in input-output models: an economic-circuit approach
2004
International audience; The Make-Use Model serves as a basis for most national accounting systems as the System of National Accounts (SNA) and is acknowledged as the most suitable model for interregional analysis. Two hypotheses are traditionally made featuring either industry-based technologies (IBT) or commodity-based technologies (CBT). While industry-based technologies can be easily interpreted in terms of a demand-driven economic circuit, it will be shown that: (1) commodity-based technologies cannot be interpreted as a demand-driven economic circuit because this involves computing the inverse of a matrix (the matrix of industry output proportions), which is either impossible or genera…
In Search for an Integrated Design Basis for Audio and Haptics
2008
Audio and haptics as interaction modalities share properties, which make them highly appropriate to be handled within a single conceptual framework. This paper outlines such framework, gaining ingredients from the literature concerning cross-modal integration and embodied cognition. The resulting framework is bound up with a concept of physical embodiment, which has been introduced within several scientific disciplines to reveal the role of bodily experience and the corresponding mental imagery as the core of meaning-creation. In addition to theoretical discussion, the contribution of the proposed approach in design is outlined.
Wannier90 as a community code: new features and applications
2019
Wannier90 is an open-source computer program for calculating maximally-localised Wannier functions (MLWFs) from a set of Bloch states. It is interfaced to many widely used electronic-structure codes thanks to its independence from the basis sets representing these Bloch states. In the past few years the development of Wannier90 has transitioned to a community-driven model; this has resulted in a number of new developments that have been recently released in Wannier90 v3.0. In this article we describe these new functionalities, that include the implementation of new features for wannierisation and disentanglement (symmetry-adapted Wannier functions, selectively-localised Wannier functions, s…
Theoretical rotational constants of MeCnN species
1990
Abstract By means of SCF HF “ab initio” calculations with STO-3G and 6-31G basis sets, the geometric parameters of methylcyanopolyynes (MeCnN n=3, 5, 7 and 9) have been obtained. B0=0.3748 GHz for MeC7N and B0=0.2708 GHz for MeC9N, with a STO-3G basis set, were obtained. Both species, unstable in the laboratory, are still undetected in the interstellar medium, although their existence is very probable.
Superalgebras with Involution or Superinvolution and Almost Polynomial Growth of the Codimensions
2018
Let A be a superalgebra with graded involution or superinvolution ∗ and let $c_{n}^{*}(A)$, n = 1,2,…, be its sequence of ∗-codimensions. In case A is finite dimensional, in Giambruno et al. (Algebr. Represent. Theory 19(3), 599–611 2016, Linear Multilinear Algebra 64(3), 484–501 2016) it was proved that such a sequence is polynomially bounded if and only if the variety generated by A does not contain the group algebra of $\mathbb {Z}_{2}$ and a 4-dimensional subalgebra of the 4 × 4 upper-triangular matrices with suitable graded involutions or superinvolutions. In this paper we study the general case of ∗-superalgebras satisfying a polynomial identity. As a consequence we classify the varie…
Algorithms for rational discrete least squares approximation
1975
In this paper an algorithm for the computation of a locally optimal polefree solution to the discrete rational least squares problem under a mild regularity condition is presented. It is based on an adaptation of projection methods [8], [12], [13], [14], [18], [19] to the modified Gaus-Newton method [4], [10]. A special device makes possible the direct handling of the infinitely many linear constraints present in this problem.
Normalizing biproportional methods
2002
International audience; Biproportional methods are used to update matrices: the projection of a matrix Z to give it the column and row sums of another matrix is R Z S, where R and S are diagonal and secure the constraints of the problem (R and S have no signification at all because they are not identified). However, normalizing R or S generates important mathematical difficulties: it amounts to put constraints on Lagrange multipliers, non negativity (and so the existence of the solution) is not guaranteed at equilibrium or along the path to equilibrium.
Fast Approximated Discriminative Common Vectors Using Rank-One SVD Updates
2013
An efficient incremental approach to the discriminative common vector (DCV) method for dimensionality reduction and classification is presented. The proposal consists of a rank-one update along with an adaptive restriction on the rank of the null space which leads to an approximate but convenient solution. The algorithm can be implemented very efficiently in terms of matrix operations and space complexity, which enables its use in large-scale dynamic application domains. Deep comparative experimentation using publicly available high dimensional image datasets has been carried out in order to properly assess the proposed algorithm against several recent incremental formulations.
Heterogeneous PBLAS: Optimization of PBLAS for Heterogeneous Computational Clusters
2008
This paper presents a package, called Heterogeneous PBLAS (HeteroPBLAS), which is built on top of PBLAS and provides optimized parallel basic linear algebra subprograms for heterogeneous computational clusters. We present the user interface and the software hierarchy of the first research implementation of HeteroPBLAS. This is the first step towards the development of a parallel linear algebra package for heterogeneous computational clusters. We demonstrate the efficiency of the HeteroPBLAS programs on a homogeneous computing cluster and a heterogeneous computing cluster.
Predicting the structure and vibrational frequencies of ethylene using harmonic and anharmonic approaches at the Kohn–Sham complete basis set limit
2016
In this work, regular convergence patterns of the structural, harmonic, and VPT2-calculated anharmonic vibrational parameters of ethylene towards the Kohn–Sham complete basis set (KS CBS) limit are demonstrated for the first time. The performance of the VPT2 scheme implemented using density functional theory (DFT-BLYP and DFT-B3LYP) in combination with two Pople basis sets (6-311++G** and 6-311++G(3df,2pd)), the polarization-consistent basis sets pc-n, aug-pc-n, and pcseg-n (n = 0, 1, 2, 3, 4), and the correlation-consistent basis sets cc-pVXZ and aug-cc-pVXZ (X = D, T, Q, 5, 6) was tested. The BLYP-calculated harmonic frequencies were found to be markedly closer than the B3LYP-calculated h…