Inexact Inverse Subspace Iteration with Preconditioning Applied to Quadratic Matrix Polynomials

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Miloud Sadkane
Keyword(s):  
Numerical Experiments ◽  
Matrix Polynomial ◽  
Linear Convergence ◽  
Post Processing ◽  
Matrix Polynomials ◽  
Subspace Iteration ◽  
Processing Step ◽  
Invariant Pair ◽  
Quadratic Matrix ◽  
Inner Iteration

Abstract An inexact variant of inverse subspace iteration is used to find a small invariant pair of a large quadratic matrix polynomial. It is shown that linear convergence is preserved provided the inner iteration is performed with increasing accuracy. A preconditioned block GMRES solver is employed as inner iteration. The preconditioner uses the strategy of “tuning” which prevents the inner iteration from increasing and therefore results in a substantial saving in costs. The accuracy of the computed invariant pair can be improved by the addition of a post-processing step involving very few iterations of Newton’s method. The effectiveness of the proposed approach is demonstrated by numerical experiments.

A Flying Gray Ball Multi-illuminant Image Dataset for Color Research

2020 ◽  
Vol 64 (5) ◽  
pp. 50411-1-50411-8
Author(s):  
Hoda Aghaei ◽  
Brian Funt
Keyword(s):  
Machine Vision ◽  
Spectral Reflectance ◽  
Color Constancy ◽  
Ground Truth ◽  
Practical Approach ◽  
Post Processing ◽  
Illumination Estimation ◽  
Processing Step ◽  
Image Dataset

Abstract For research in the field of illumination estimation and color constancy, there is a need for ground-truth measurement of the illumination color at many locations within multi-illuminant scenes. A practical approach to obtaining such ground-truth illumination data is presented here. The proposed method involves using a drone to carry a gray ball of known percent surface spectral reflectance throughout a scene while photographing it frequently during the flight using a calibrated camera. The captured images are then post-processed. In the post-processing step, machine vision techniques are used to detect the gray ball within each frame. The camera RGB of light reflected from the gray ball provides a measure of the illumination color at that location. In total, the dataset contains 30 scenes with 100 illumination measurements on average per scene. The dataset is available for download free of charge.

scholarly journals A fast $$(2 + \frac{2}{7})$$-approximation algorithm for capacitated cycle covering

2021 ◽  
Author(s):  
Vera Traub ◽  
Thorben Tröbst
Keyword(s):  
Vehicle Routing Problem ◽  
Covering Problem ◽  
Post Processing ◽  
Routing Problem ◽  
Cycle Cover ◽  
Disjoint Cycles ◽  
Processing Step ◽  
Number Of Cycles ◽  
Vertex Disjoint ◽  
Capacitated Vehicle

AbstractWe consider the capacitated cycle covering problem: given an undirected, complete graph G with metric edge lengths and demands on the vertices, we want to cover the vertices with vertex-disjoint cycles, each serving a demand of at most one. The objective is to minimize a linear combination of the total length and the number of cycles. This problem is closely related to the capacitated vehicle routing problem (CVRP) and other cycle cover problems such as min-max cycle cover and bounded cycle cover. We show that a greedy algorithm followed by a post-processing step yields a $$(2 + \frac{2}{7})$$ ( 2 + 2 7 ) -approximation for this problem by comparing the solution to a polymatroid relaxation. We also show that the analysis of our algorithm is tight and provide a $$2 + \epsilon $$ 2 + ϵ lower bound for the relaxation.

A general inverse matrix series relation and associated polynomials – II

2021 ◽  
Vol 71 (2) ◽  
pp. 301-316
Author(s):  
Reshma Sanjhira
Keyword(s):  
Matrix Polynomial ◽  
Combinatorial Identities ◽  
Inverse Matrix ◽  
Matrix Polynomials ◽  
Special Cases ◽  
Series Representations ◽  
The Matrix ◽  
Associated Polynomials ◽  
Matrix Pair ◽  
Matrix Series

Abstract We propose a matrix analogue of a general inverse series relation with an objective to introduce the generalized Humbert matrix polynomial, Wilson matrix polynomial, and the Rach matrix polynomial together with their inverse series representations. The matrix polynomials of Kiney, Pincherle, Gegenbauer, Hahn, Meixner-Pollaczek etc. occur as the special cases. It is also shown that the general inverse matrix pair provides the extension to several inverse pairs due to John Riordan [An Introduction to Combinatorial Identities, Wiley, 1968].

scholarly journals Folding photopolymerized origami sheets by post-curing

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Xiaodong He ◽  
Christopher-Denny Matte ◽  
Tsz-Ho Kwok
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Stress Distribution ◽  
Maximum Principal Stress ◽  
Second Step ◽  
Post Processing ◽  
Element Analysis ◽  
Digital Light Processing ◽  
Processing Step ◽  
Lower Maximum

AbstractThe paper presents a novel manufacturing approach to fabricate origami based on 3D printing utilizing digital light processing. Specifically, we propose to leave part of the model uncured during the printing step, and then cure it in the post-processing step to set the shape in a folded configuration. While the cured regions in the first step try to regain their unfolded shape, the regions cured in the second step attempt to keep their folded shape. As a result, the final shape is obtained when both regions’ stresses reach equilibrium. Finite element analysis is performed in ANSYS to obtain the stress distribution on common hinge designs, demonstrating that the square-hinge has a lower maximum principal stress than elliptical and triangle hinges. Based on the square-hinge and rectangular cavity, two variables—the hinge width and the cavity height—are selected as principal variables to construct an empirical model with the final folding angle. In the end, experimental verification shows that the developed method is valid and reliable to realize the proposed deformation and 3D development of 2D hinges.

scholarly journals Enhanced Convolutional-Neural-Network Architecture for Crop Classification

2021 ◽  
Vol 11 (9) ◽  
pp. 4292
Author(s):  
Mónica Y. Moreno-Revelo ◽  
Lorena Guachi-Guachi ◽  
Juan Bernardo Gómez-Mendoza ◽  
Javier Revelo-Fuelagán ◽  
Diego H. Peluffo-Ordóñez
Keyword(s):  
Neural Network ◽  
Convolutional Neural Network ◽  
Network Architecture ◽  
Classification Model ◽  
Classification Error ◽  
Small Scale ◽  
Post Processing ◽  
Average Accuracy ◽  
Processing Step ◽  
Crop Classification

Automatic crop identification and monitoring is a key element in enhancing food production processes as well as diminishing the related environmental impact. Although several efficient deep learning techniques have emerged in the field of multispectral imagery analysis, the crop classification problem still needs more accurate solutions. This work introduces a competitive methodology for crop classification from multispectral satellite imagery mainly using an enhanced 2D convolutional neural network (2D-CNN) designed at a smaller-scale architecture, as well as a novel post-processing step. The proposed methodology contains four steps: image stacking, patch extraction, classification model design (based on a 2D-CNN architecture), and post-processing. First, the images are stacked to increase the number of features. Second, the input images are split into patches and fed into the 2D-CNN model. Then, the 2D-CNN model is constructed within a small-scale framework, and properly trained to recognize 10 different types of crops. Finally, a post-processing step is performed in order to reduce the classification error caused by lower-spatial-resolution images. Experiments were carried over the so-named Campo Verde database, which consists of a set of satellite images captured by Landsat and Sentinel satellites from the municipality of Campo Verde, Brazil. In contrast to the maximum accuracy values reached by remarkable works reported in the literature (amounting to an overall accuracy of about 81%, a f1 score of 75.89%, and average accuracy of 73.35%), the proposed methodology achieves a competitive overall accuracy of 81.20%, a f1 score of 75.89%, and an average accuracy of 88.72% when classifying 10 different crops, while ensuring an adequate trade-off between the number of multiply-accumulate operations (MACs) and accuracy. Furthermore, given its ability to effectively classify patches from two image sequences, this methodology may result appealing for other real-world applications, such as the classification of urban materials.

scholarly journals Evolution of the Microstructure and Mechanical Properties of a Ti35Nb2Sn Alloy Post-Processed by Hot Isostatic Pressing for Biomedical Applications

Metals ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 1027
Author(s):  
Joan Lario ◽  
Ángel Vicente ◽  
Vicente Amigó
Keyword(s):  
Powder Metallurgy ◽  
Mechanical Strength ◽  
Room Temperature ◽  
Hot Isostatic Pressing ◽  
Phase Changes ◽  
Post Processing ◽  
Isostatic Pressing ◽  
Porosity Reduction ◽  
Processing Step ◽  
Hip Process

The HIP post-processing step is required for developing next generation of advanced powder metallurgy titanium alloys for orthopedic and dental applications. The influence of the hot isostatic pressing (HIP) post-processing step on structural and phase changes, porosity healing, and mechanical strength in a powder metallurgy Ti35Nb2Sn alloy was studied. Powders were pressed at room temperature at 750 MPa, and then sintered at 1350 °C in a vacuum for 3 h. The standard HIP process at 1200 °C and 150 MPa for 3 h was performed to study its effect on a Ti35Nb2Sn powder metallurgy alloy. The influence of the HIP process and cold rate on the density, microstructure, quantity of interstitial elements, mechanical strength, and Young’s modulus was investigated. HIP post-processing for 2 h at 1200 °C and 150 MPa led to greater porosity reduction and a marked retention of the β phase at room temperature. The slow cooling rate during the HIP process affected phase stability, with a large amount of α”-phase precipitate, which decreased the titanium alloy’s yield strength.

scholarly journals Relevance of processing parameters for grain growth of metal halide perovskites with nanoimprint

2021 ◽  
Vol 127 (9) ◽  
Author(s):  
Andre Mayer ◽  
Tobias Haeger ◽  
Manuel Runkel ◽  
Johannes Rond ◽  
Johannes Staabs ◽  
...  
Keyword(s):  
Grain Size ◽  
Grain Growth ◽  
Secondary Growth ◽  
Processing Parameters ◽  
Post Processing ◽  
Perovskite Layer ◽  
Processing Step ◽  
Similar Preparation ◽  
Materials Used ◽  
Log Normal

AbstractThe quality and the stability of devices prepared from polycrystalline layers of organic–inorganic perovskites highly depend on the grain sizes prevailing. Tuning of the grain size is either done during layer preparation or in a post-processing step. Our investigation refers to thermal imprint as the post-processing step to induce grain growth in perovskite layers, offering the additional benefit of providing a flat surface for multi-layer devices. The material studied is MAPbBr3; we investigate grain growth at a pressure of 100 bar and temperatures of up to 150 °C, a temperature range where the pressurized stamp is beneficial to avoid thermal degradation. Grain coarsening develops in a self-similar way, featuring a log-normal grain size distribution; categories like ‘normal’ or ‘secondary’ growth are less applicable as the layers feature a preferential orientation already before imprint-induced grain growth. The experiments are simulated with a capillary-based growth law; the respective parameters are determined experimentally, with an activation energy of Q ≈ 0.3 eV. It turns out that with imprint as well the main parameter relevant to grain growth is temperature; to induce grain growth in MAPbBr3 within a reasonable processing time a temperature of 120 °C and beyond is advised. An analysis of the mechanical situation during imprint indicates a dominance of thermal stress. The minimization of elastic energy and surface energy together favours the development of grains with (100)-orientation in MaPbBr3 layers. Furthermore, the experiments indicate that the purity of the materials used for layer preparation is a major factor to achieve large grains; however, a diligent and always similar preparation of the layer is equally important as it defines the pureness of the resulting perovskite layer, intimately connected with its capability to grow. The results are not only of interest to assess the potential of a layer with respect to grain growth when specific temperatures and times are chosen; they also help to rate the long-term stability of a layer under temperature loading, e.g. during the operation of a device.

scholarly journals A Schur-Cohn theorem for matrix polynomials

1990 ◽  
Vol 33 (3) ◽  
pp. 337-366 ◽  
Author(s):  
Harry Dym ◽  
Nicholas Young
Keyword(s):  
Unit Circle ◽  
Matrix Polynomial ◽  
Hermitian Matrix ◽  
Krein Space ◽  
Gram Matrix ◽  
Natural Basis ◽  
Test Matrix ◽  
Matrix Polynomials ◽  
Rational Vector ◽  
Square Matrix

Let N(λ) be a square matrix polynomial, and suppose det N is a polynomial of degree d. Subject to a certain non-singularity condition we construct a d by d Hermitian matrix whose signature determines the numbers of zeros of N inside and outside the unit circle. The result generalises a well known theorem of Schur and Cohn for scalar polynomials. The Hermitian “test matrix” is obtained as the inverse of the Gram matrix of a natural basis in a certain Krein space of rational vector functions associated with N. More complete results in a somewhat different formulation have been obtained by Lerer and Tismenetsky by other methods.

Finding Approximate Shape Regularities for Reverse Engineering

2001 ◽  
Vol 1 (4) ◽  
pp. 282-290 ◽  
Author(s):  
F. C. Langbein ◽  
B. I. Mills ◽  
A. D. Marshall ◽  
R. R. Martin
Keyword(s):  
Reverse Engineering ◽  
Small Groups ◽  
Input Data ◽  
Boundary Representation ◽  
Range Data ◽  
Engineering Systems ◽  
Post Processing ◽  
Processing Step ◽  
3D Range Data

Current reverse engineering systems can generate boundary representation (B-rep) models from 3D range data. Such models suffer from inaccuracies caused by noise in the input data and algorithms. The quality of reverse engineered geometric models can be improved by finding candidate shape regularities in such a model, and constraining the model to meet a suitable subset of them, in a post-processing step called beautification. This paper discusses algorithms to detect such approximate regularities in terms of similarities between feature objects describing properties of faces, edges and vertices, and small groups of these elements in a B-rep model with only planar, spherical, cylindrical, conical and toroidal faces. For each group of similar feature objects they also seek special feature objects which may represent the group, e.g. an integer value which approximates the radius of similar cylinders. Experiments show that the regularities found by the algorithms include the desired regularities as well as spurious regularities, which can be limited by an appropriate choice of tolerances.

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