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Matrix factoring by fraction-free reduction
[article]
2016
arXiv
pre-print
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We show that existing fraction-free QR (Gram-Schmidt) algorithms create a common factor in the last column of Q. ...
We consider exact matrix decomposition by Gauss-Bareiss reduction. We investigate two aspects of the process: common row and column factors and the influence of pivoting strategies. ...
ACKNOWLEDGMENTS This work was supported in part by the Austrian Science Fund (FWF) grant SFB50 (F5009-N15). We would like to thank Prof. Kevin G. Hare and Univ.-Doz. Dr. Arne Winterhof for helpful. ...
arXiv:1603.03565v1
fatcat:2oadvujymrfqxklx7edp4mfpee
Common Factors in Fraction-Free Matrix Decompositions
[article]
2020
arXiv
pre-print
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We show that fraction-free Gauss--Bareiss reduction leads to triangular matrices having a non-trivial number of common row factors. ...
Similar observations apply to the common factors in a fraction-free QR decomposition. Our conclusions are tested experimentally. ...
In particular, the statements of Corollary 8 and Theorem 14 were pointed out by one of the referees. ...
arXiv:2005.12380v1
fatcat:yrhimv5oj5fwln7qeyyl5yjaha
Common Factors in Fraction-Free Matrix Decompositions
2020
Mathematics in Computer Science
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Similar observations apply to the common factors in a fraction-free QR decomposition. Our conclusions are tested experimentally. ...
We show that fraction-free Gauß–Bareiss reduction leads to triangular matrices having a non-trivial number of common row factors. We identify two types of common factors: systematic and statistical. ...
The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. ...
doi:10.1007/s11786-020-00495-9
fatcat:zozlrr7forhrxl7d2sdj2kvnd4
Scratchpad's view of algebra II
1991
Proceedings of the 1991 international symposium on Symbolic and algebraic computation - ISSAC '91
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The consequence of the algorithms and interfaces presented in this paper is that Scratchpad can factorize in any extension of the integers or finite fields by any combination of polynomial, fraction and ...
or Fraction. ...
The reduction to square-free polynomials is simple [Yun, 1976; 1977] . ...
doi:10.1145/120694.120699
dblp:conf/issac/DavenportGT91
fatcat:cev6rdiqkfgkxe33kvx26sjtkm
Euro Money Market Spreads During the 2007-? Financial Crisis
2011
Social Science Research Network
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By means of a novel Fractionally Integrated Heteroskedastic Factor Vector Autoregressive model, we ...nd evidence of a deterministic level factor in the EURIBOR-OIS (OIS) spreads term structure, associated ...
Key words: money market interest rates, credit/liquidity risk, fractionally integrated heteroskedastic factor vector autoregressive model. JEL classi...cation: C32, E43, E58, G15. ...
First, a new estimate of the m common deterministic factors and their factor loading matrix can be obtained by the application of PCA to the (new) long memory-free series x t
Figure 1 : 1 level factor ...
doi:10.2139/ssrn.1604694
fatcat:knlzjcf33jaybdghlmhr5jaqs4
Euro money market spreads during the 2007–? financial crisis
2012
Journal of Empirical Finance
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By means of a novel Fractionally Integrated Heteroskedastic Factor Vector Autoregressive model, we ...nd evidence of a deterministic level factor in the EURIBOR-OIS (OIS) spreads term structure, associated ...
with the two waves of stress in the interbank market, following the BNP Paribas (9 August 2007) and the Lehman Brothers (16 September 2008) "shocks", and two additional factors, of the long memory type ...
m n, with n m matrix of loadings ; f t is a r-variate vector of heteroskedastic fractionally integrated common factors, r n, of order d i in mean and b i in variance, with 0 < d i < 1, 0 < b i < 1; i = ...
doi:10.1016/j.jempfin.2012.04.003
fatcat:3bhyujjikzeexmkjsgnd4t2xbe
MO-A-217BCD-02: Yttrium-90 Microsphere Therapy Planning and Dose Calculations
2012
Medical Physics (Lancaster)
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Cheenu Kappadath, PhD
Lung-Shunt Fraction Modification
Lung Shunting
Reduction Factor
<10 %
No Reduction
10 % -15 %
20 % reduction
15 % -20 %
40 % reduction
> 20 %
No Treatment
Lung ...
50
SIR-Spheres
Lung Shunting
Reduction Factor
<10 %
No Reduction
10 % -15 %
20 % reduction
15 % -20 %
40 % reduction
> 20 %
No Treatment
Lung dose per treatment < 25 Gy
(Ho et al, ...
doi:10.1118/1.4735751
pmid:28517496
fatcat:ouxgyiw3vbcwhmt4ihvd7enyxy
A Practical Implementation of a Modular Algorithm for Ore Polynomial Matrices
[chapter]
2014
Computer Mathematics
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and fraction-free versions. ...
We briefly review a modular algorithm to perform row reduction of a matrix of Ore polynomials with coefficients in Z[t], and describe a practical implementation in Maple that improves over previous modular ...
After removing some common factors in each row to reduce the results, the resulting matrix is . The order basis M(Z) of degree µ = (2, 2) and order ω = (3, 3) can be easily extracted. ...
doi:10.1007/978-3-662-43799-5_5
dblp:conf/ascm/ChengL09
fatcat:rgnfx3yvgff4pc2aoujh6mioeq
Which pivot to solve linear systems?
2002
Journal of Computational and Applied Mathematics
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Exact calculations instead of approximated ones have been implemented with 2% of runtime overcost in our example. ...
The fraction-free pivot revisited We have already got rid of the calculation of the whole triangular matrix required by the new fraction-free pivot in Section 4.1. ...
The division-free pivot A common and intuitive idea to handle integers consists in performing divisions only with greatest common divisors. ...
doi:10.1016/s0377-0427(02)00482-x
fatcat:5cos7cnnxva77jngqrgh4fe7bi
Tissue Augmentation with Allograft Adipose Matrix For the Diabetic Foot in Remission
2017
Plastic and Reconstructive Surgery, Global Open
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After healing, recurrence is common. Modulating plantar pressure has been associated with extension of ulcer free days. ...
This may ultimately assist the clinician in extending ulcer-free days for patients in diabetic foot remission. ...
of glucose and lipid metabolism. 16, 17 When implanted in preclinical models, the natural factors that are retained in the matrix support host cell infiltration and revascularization of the matrix ( ...
doi:10.1097/gox.0000000000001555
pmid:29184753
pmcid:PMC5682189
fatcat:rw4risfbbrf6lmaqk45j6lklda
Research on Structural Vibration Control Based on Local Stiffness Reinforcement and Local Constrained Damping
2019
Proceedings of the ICA congress
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This method has significance for structures with high requirements for weight and vibration control in engineering. ...
Based on harmonic response analysis, the technology of design with stiffness and damping for vibration control is studied in this paper. ...
Rational fractional derivative model has just been developed in recent decades. ...
doi:10.18154/rwth-conv-239087
fatcat:a5r6vcewxfcfneqyglkndxhkom
Chemotaxis and haptotaxis of human malignant mesothelioma cells: effects of fibronectin, laminin, type IV collagen, and an autocrine motility factor-like substance
1993
Cancer Research
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We also analyzed STAV cell serum-free conditioned medium with respect to the possible presence of "autocrine motility factor-like" substance. ...
proteins in vitro. ...
Therefore we conclude that the motility factor in M, 67,000 fractions must be produced by STAV cells. ...
pmid:8364933
fatcat:xk46fktuibfv7a4nfns2qkgtxi
MODULAR COMPUTATION FOR MATRICES OF ORE POLYNOMIALS
2007
Computer Algebra 2006
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We give a modular algorithm to perform row reduction of a matrix of Ore polynomials with coefficients in Z[t]. Both the transformation matrix and the transformed matrix are computed. ...
Our algorithms improve on existing fraction-free algorithms and can be viewed as generalizations of the work of Li and Nemes on GCRDs and LCLMs of Ore polynomials. ...
When the matrix entries are shift polynomials, we obtained fraction-free algorithms for computing row-reduced and weak Popov forms, and for computing a greatest common right divisor (GCRD) or a least common ...
doi:10.1142/9789812778857_0004
fatcat:gfsgrov4xrasxgvoghuoadcrae
Fraction-free computation of matrix Padé systems
1997
Proceedings of the 1997 international symposium on Symbolic and algebraic computation - ISSAC '97
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We present a fraction-free approach to the computation of matrix Padé systems. ...
By using this modified Schur complement for these matrices we are able to obtain a fast hybrid fraction-free algorithm for their computation. ...
smaller problems, multiplying the two matrix polynomials and then dividing out by the known common factor ±c 2sr . ...
doi:10.1145/258726.258765
fatcat:74b6yrv4drgdxopza3yvfkqxh4
Ni–Fe–Al2O3 electrodeposited nanocomposite coating with functionally graded microstructure
2016
Bulletin of Materials Science
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Investigating the best coatings obtained from both above methods exhibited 50 and 20% reduction in corrosion current density and wear rate, respectively, for DDM specimen in comparison to FIM sample. ...
free surface of the coating and its amount was gradually decreased to the interface. ...
Taking into account of these descriptions, increasing of nanoparticle fraction as well as the raising of Ni in the matrix due to duty cycle reduction is the main efficacious criteria on the increase of ...
doi:10.1007/s12034-016-1211-1
fatcat:7trjpelifzdb7efaxv62eumckq
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