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We present a fast randomized algorithm that computes a low rank LU decomposition. Our algorithm uses random projections type techniques to efficiently compute a low rank approximation of large matrices. The randomized LU algorithm can be…

Numerical Analysis · Mathematics 2016-02-02 Gil Shabat , Yaniv Shmueli , Yariv Aizenbud , Amir Averbuch

Three algorithms of Gram-Schmidt type are given that produce an orthogonal decomposition of finite $d$-dimensional symmetric, alternating, or Hermitian forms over division rings. The first uses $d^3/3+O(d^2)$ ring operations with very…

Numerical Analysis · Mathematics 2020-11-23 James B. Wilson

In this paper, a three-dimensional light detection and ranging simultaneous localization and mapping (SLAM) method is proposed that is available for tracking and mapping with 500--1000 Hz processing. The proposed method significantly…

Robotics · Computer Science 2021-03-02 Masashi Yokozuka , Kenji Koide , Shuji Oishi , Atsuhiko Banno

This paper considers fast algorithms for operations on linearized polynomials. We propose a new multiplication algorithm for skew polynomials (a generalization of linearized polynomials) which has sub-quadratic complexity in the polynomial…

Symbolic Computation · Computer Science 2017-07-12 Sven Puchinger , Antonia Wachter-Zeh

Arclength continuation and branch switching are enormously successful algorithms for the computation of bifurcation diagrams. Nevertheless, their combination suffers from three significant disadvantages. The first is that they attempt to…

Numerical Analysis · Mathematics 2016-03-03 Patrick E. Farrell , Casper H. L. Beentjes , Ásgeir Birkisson

An efficient decoding algorithm named `divided decoder' is proposed in this paper. Divided decoding can be combined with any decoder using QR-decomposition and offers different pairs of performance and complexity. Divided decoding provides…

Information Theory · Computer Science 2009-01-23 In Sook Park

The simultaneous localization and mapping (SLAM) problem is considered in three dimensions. The proposed algorithm, differential geometric SLAM (DG-SLAM), employs methods from differential geometry to propagate the state and map estimates.…

Robotics · Computer Science 2015-06-02 David Evan Zlotnik , James Richard Forbes

We consider a new semidefinite programming relaxation for directed edge expansion, which is obtained by adding triangle inequalities to the reweighted eigenvalue formulation. Applying the matrix multiplicative weight update method to this…

Data Structures and Algorithms · Computer Science 2023-06-16 Lap Chi Lau , Kam Chuen Tung , Robert Wang

State-of-the-art techniques for simultaneous localization and mapping (SLAM) employ iterative nonlinear optimization methods to compute an estimate for robot poses. While these techniques often work well in practice, they do not provide…

Robotics · Computer Science 2015-07-21 Luca Carlone , David Rosen , Giuseppe Calafiore , John Leonard , Frank Dellaert

A unified method for three-dimensional reconstruction of objects from transmission images collected at multiple illumination directions is described. The method may be applicable to experimental conditions relevant to absorption-based,…

Medical Physics · Physics 2022-12-07 Timur E. Gureyev , Hamish G. Brown , Harry M. Quiney , Leslie J. Allen

We describe a heuristic algorithm for computing treedepth decompositions, submitted for the PACE 2020 challenge. It relies on a variety of greedy algorithms computing elimination orderings, as well as a Divide & Conquer approach on balanced…

Data Structures and Algorithms · Computer Science 2020-10-01 Marcin Wrochna

Modern LiDAR-SLAM (L-SLAM) systems have shown excellent results in large-scale, real-world scenarios. However, they commonly have a high latency due to the expensive data association and nonlinear optimization. This paper demonstrates that…

Robotics · Computer Science 2021-03-25 Jianhao Jiao , Yilong Zhu , Haoyang Ye , Huaiyang Huang , Peng Yun , Linxin Jiang , Lujia Wang , Ming Liu

Although there is ample work in the literature dealing with skewness in the multivariate setting, there is a relative paucity of work in the matrix variate paradigm. Such work is, for example, useful for modelling three-way data. A matrix…

Methodology · Statistics 2017-10-09 Michael P. B. Gallaugher , Paul D. McNicholas

We describe an algorithm for fast multiplication of skew polynomials. It is based on fast modular multiplication of such skew polynomials, for which we give an algorithm relying on evaluation and interpolation on normal bases. Our…

Symbolic Computation · Computer Science 2017-02-07 Xavier Caruso , Jérémy Le Borgne

In this article we present first an algorithm for calculating the determining equations associated with so-called ``nonclassical method'' of symmetry reductions (a la Bluman and Cole) for systems of partial differentail equations. This…

solv-int · Physics 2008-02-03 Peter A. Clarkson , Elizabeth L. Mansfield

A family of the Block Matching 3-D (BM3D) algorithms for various imaging problems has been recently proposed within the framework of nonlocal patch-wise image modeling [1], [2]. In this paper we construct analysis and synthesis frames,…

Optimization and Control · Mathematics 2015-05-28 Aram Danielyan , Vladimir Katkovnik , Karen Egiazarian

The aim of this work is to develop a fast algorithm for approximating the matrix function $f(A)$ of a square matrix $A$ that is symmetric and has hierarchically semiseparable (HSS) structure. Appearing in a wide variety of applications,…

Numerical Analysis · Mathematics 2024-02-28 Angelo A. Casulli , Daniel Kressner , Leonardo Robol

We generalize Fulton's determinantal construction of Schur modules to the skew setting, providing an explicit and functorial presentation using only elementary linear algebra and determinantal identities, in parallel with the partition…

Combinatorics · Mathematics 2025-11-06 Reuven Hodges , Hanzhang Yin

This paper serves as our first effort to develop a new triangular spectral element method (TSEM) on unstructured meshes, using the rectangle-triangle mapping proposed in the conference note [21]. Here, we provide some new insights into the…

Numerical Analysis · Mathematics 2012-04-24 Michael Daniel Samson , Huiyuan Li , Li-Lian Wang

The deterministic recursive pivot-free algorithms for the computation of generalized Bruhat decomposition of the matrix in the field and for the computation of the inverse matrix are presented. This method has the same complexity as…

Symbolic Computation · Computer Science 2017-02-24 Gennadi Malaschonok