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Simplified decision making in the belief space using belief sparsification [article]

Khen Elimelech, Vadim Indelman
2021 arXiv   pre-print
We claim that one can often generate and solve an analogous yet simplified decision problem, which can be solved more efficiently.  ...  Typically, to solve a decision problem, one should identify the optimal action from a set of candidates, according to some objective.  ...  Andrej Kitanov from the Faculty of Aerospace Engineering at the Technion -Israel Institute of Technology, for insightful discussions concerning Section 3.3.2, and his assistance with implementing the simulation  ... 
arXiv:1909.00885v4 fatcat:gur4uqitdng7zimopzenivv5re

I-binomial scrambling of digital nets and sequences

Shu Tezuka, Henri Faure
2003 Journal of Complexity  
Anal. 34 (1997) 1884) remains valid with the left ibinomial scrambling, and thereby conclude that all the results on the expected errors of the integration problem so far obtained with Owen's scrambling  ...  In this setting, we assume some sample space of integration rules from which we randomly choose one.  ...  Acknowledgments We thank Anargyros Papageorgiou and Art Owen for many valuable comments and helpful discussions on the first draft.  ... 
doi:10.1016/s0885-064x(03)00035-9 fatcat:jmnx4ycafrgg5eamzugusn2smy

Parallel Processing Model for Cholesky Decomposition Algorithm in AlgoWiki Project

2016 Supercomputing Frontiers and Innovations  
The comprehensive analysis of algorithmic properties of well-known Cholesky decomposition is performed on the basis of multifold AlgoWiki technologies.  ...  The comprehension of the parallel algorithm structure enable us to implement efficiently the algorithm at hardware platform specified.  ...  This paper is distributed under the terms of the Creative Commons Attribution-Non Commercial 3.0 License which permits non-commercial use, reproduction and distribution of the work without further permission  ... 
doi:10.14529/jsfi160307 fatcat:yvjcte3ywnchpai5gvz7f5dypa

Efficient Cholesky Factor Recovery for Column Reordering in Simultaneous Localisation and Mapping

S. Touchette, W. Gueaieb, E. Lanteigne
2016 Journal of Intelligent and Robotic Systems  
To obtain the least square solution of such systems efficiently, it is desired to maintain a good column ordering such that fill-ins are reduced.  ...  In this article, it is shown that the Cholesky factorisation of an updated matrix can be efficiently recovered from the previous factorisation if the permutations are localised.  ...  There is one variable node (circle) and matrix column associated with each unknown (pose or landmark). There is one factor node (square) and matrix row associated with each measurement.  ... 
doi:10.1007/s10846-016-0367-7 fatcat:52zq75bcxre23ijo3qgtfrraxm

Adaptive partitioning techniques for ordinary differential equations

Stig Skelboe
2006 BIT Numerical Mathematics  
This paper presents an adaptive partitioning algorithm based on a classical graph algorithm and techniques for the efficient evaluation of the error introduced by the partitioning.  ...  In this paper the objective of the partitioning is to permit the numerical integration of one time step to be performed as the solution of a sequence of small subproblems.  ...  Apply the same reordering to B resulting in B which can then readily be partitioned into a lower block triangular matrix D with the same envelope as B δ and the upper block triangular (without diagonal  ... 
doi:10.1007/s10543-006-0074-z fatcat:rxzvf6kjifaqjiw6hnanxcucle

Smoothing, splines and smoothing splines; Their application in geomagnetism

C.G Constable, R.L Parker
1988 Journal of Computational Physics  
We discuss the use of smoothing splines (SS) and least squares splines (LSS) in nonparametric regression on geomagnetic data.  ...  The computational efficiency of the least squares spline may be retained and its principal disadvantage overcome, by adding a penalty term in the square of the second derivative to the minimized functional  ...  The first term in (3) can be written as where R E M(L x L) is an upper triangular matrix, the upper square portion of the right factor in the QR decompositions of B; y1 E lRL is the upper part of the  ... 
doi:10.1016/0021-9991(88)90062-9 fatcat:7vefpaahvnbdvhilditeykothy

Global Positioning System Integer Ambiguity Resolution Using Factorized Least-Squares Techniques

Mark L. Psiaki, Shan Mohiuddin
2007 Journal of Guidance Control and Dynamics  
The square, upper-triangular matrix Roy, = PinyR~! Piny is a Square root of the covariance matrix for the real-valued version of the reordered ambiguity vector P;,,,.1.  ...  problem’s upper-triangular square-root information matrix.  ... 
doi:10.2514/1.21982 fatcat:2tfzbrg2ofcp3baew35nttbw54

From Bareiss' algorithm to the stable computation of partial correlations

Jean-Marc Delosme, Ilse C.F. Ipsen
1989 Journal of Computational and Applied Mathematics  
For symmetric positive-definite matrices B, the normalized version of Bareiss' algorithm is the Hyperbolic Cholesky algorithm, which computes the upper and lower triangular Cholesky factors U and L of  ...  In that method one computes the QR decomposition A = QU of the data matrix and applies orthogonal rotations to transform U to L; the sines of the rotation angles constitute a set of partial correlation  ...  Acknowledgement We would like to thank referee # 1 for pointing out the connection to the algorithms in [8, 13] .  ... 
doi:10.1016/0377-0427(89)90361-0 fatcat:uzkqr66j7nezzjsfahpbiemr4u

Hierarchical Orthogonal Factorization: Sparse Least Squares Problems [article]

Abeynaya Gnanasekaran, Eric Darve
2021 arXiv   pre-print
The end result is an approximate factorization of the matrix stored as a sequence of sparse orthogonal and upper-triangular factors and hence easy to apply/solve with a vector.  ...  Our algorithm is built on top of a Nested Dissection based multifrontal QR approach.  ...  orthogonal or sparse upper triangular matrix.  ... 
arXiv:2102.09878v2 fatcat:oyetnh76anesvho2bki3zj7se4

H-matrix Preconditioners in Convection-Dominated Problems

Sabine Le Borne, Lars Grasedyck
2006 SIAM Journal on Matrix Analysis and Applications  
Whereas the approximation of the matrix inverse by an H-matrix requires some modification in the underlying index clustering when applied to convectiondominant problems, the H-LU -decomposition works well  ...  In this paper we exploit H-matrix techniques to approximate the LU -decompositions of stiffness matrices as they appear in (finite element or finite difference) discretizations of convectiondominated elliptic  ...  The triangular solve involving an upper triangular matrix follows analogously.  ... 
doi:10.1137/040615845 fatcat:5c2icoubirdbzkkajbsmfctkwu

Efficient Factor Graph Fusion for Multi-Robot Mapping and Beyond

Ramkumar Natarajan, Michael A. Gennert
2018 2018 21st International Conference on Information Fusion (FUSION)  
Nevertheless, the square-root factor R r is upper triangular and not a symmetric matrix.  ...  Updating the square root factor with a new measurement removes its upper triangularity. It is made upper triangular again by using Givens rotations [17] .  ...  In reality the robot motion is subjected to noise and hence the actual velocity differ from the commanded one.  ... 
doi:10.23919/icif.2018.8455502 dblp:conf/fusion/NatarajanG18 fatcat:nbsoqnpwjjf3vpep4ywaapyd7u

Computer analysis of large structural systems

R. BAMFORD, T. LANG, R. MELOSH, L. SCHMELE
1969 Journal of Spacecraft and Rockets  
No reordering would reduce the maximum bandwidth. The matrix to be decomposed was generated by multiply- ing an upper triangular matrix by its transpose.  ...  In addition, since K is symmetric, only the upper triangular or lower triangular part of K need be stored on tape and read into core.  ... 
doi:10.2514/3.29677 fatcat:rx5pmnu6hnfdjdqyhb5wkq3t7q

Computational complexities and storage requirements of some Riccati equation solvers

SENOL UTKU, JOHN A. GARBA, A. V. RAMESH
1989 Journal of Guidance Control and Dynamics  
Continuous Square-Root Algorithms Continuous square-root algorithms'’.6-37-8 give differential equation for the square root of the Riccati matrix.  ...  ., ‘‘An Algorithm for Propagating the Square-Root Covariance Matrix in Triangular Form’’, /EEE Transactions on Automatic Control, Vol. AC-21, Feb. 1976, pp. 122-123.  ... 
doi:10.2514/3.20434 fatcat:gzpgvt25cnhvfesstrewg56gd4

Computing matrix functions

Nicholas J. Higham, Awad H. Al-Mohy
2010 Acta Numerica  
The survey is organized by classes of methods, which are broadly those based on similarity transformations, those employing approximation by polynomial or rational functions, and matrix iterations.  ...  The need to evaluate a function f (A) ∈ C n×n of a matrix A ∈ C n×n arises in a wide and growing number of applications, ranging from the numerical solution of differential equations to measures of the  ...  Cost of Padé versus Taylor approximants within the scaling and squaring method  ... 
doi:10.1017/s0962492910000036 fatcat:oe43p5qwtzhxhbj5imwplynewq

Automatic element reordering for finite element analysis with frontal solution schemes

S. W. Sloan, M. F. Randolph
1983 International Journal for Numerical Methods in Engineering  
This intermediate step is necessary because of the nature of the frontal solution procedure, which assembles variables on an element-by-element basis but eliminates them node by node.  ...  The procedure is shown to generate efficient element numberings for a wide variety of test examples.  ...  Britto in providing the data for some of the test examples, as well as continual discussion on the topic of renumbering finite element meshes, is gratefully acknowledged.  ... 
doi:10.1002/nme.1620190805 fatcat:bpqa76m7pza5hhebyflpvov5ua
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