Selection of fictitious independent variables for the solution of sparse linear equations

1991 ◽  
Vol 42 (3) ◽  
pp. 431-444
Author(s):  
H. L. Abdel-Malek ◽  
S. A. El-Bardissy
Keyword(s):  
Linear Equations ◽  
Independent Variables ◽  
Selection Of

A Systematic Method for the Selection of Independent Variables in the Investigation of Complex Systems

1988 ◽  
Vol 32 (17) ◽  
pp. 1179-1182 ◽  
Author(s):  
P. Jay Merkle ◽  
Douglas B. Beaudet ◽  
Robert C. Williges ◽  
David W. Herlong ◽  
Beverly H. Williges
Keyword(s):  
Large Scale ◽  
Subjective Ratings ◽  
Systematic Method ◽  
Independent Variables ◽  
Integrated Strategy ◽  
Literature Reviews ◽  
Systematic Methodology ◽  
Research Problems ◽  
Inquiry System ◽  
Selection Of

This paper describes a systematic methodology for selecting independent variables to be considered in large-scale research problems. Five specific procedures including brainstorming, prototype interface representation, feasibility/relevance analyses, structured literature reviews, and user subjective ratings are evaluated and incorporated into an integrated strategy. This methodology is demonstrated in the context of designing the user interface for a telephone-based information inquiry system. The procedure was successful in reducing an initial set of 95 independent variables to a subset of 19 factors that warrant subsequent detailed analysis. These results are discussed in terms of a comprehensive sequential research methodology useful for investigating human factors problems.

Comparative Thermodynamics for Brayton and Rankine Cycles

1990 ◽  
Vol 112 (1) ◽  
pp. 94-99 ◽  
Author(s):  
E. W. Beans
Keyword(s):  
Thermodynamic Model ◽  
Thermal Efficiency ◽  
Unit Volume ◽  
Work Conditions ◽  
Comparison Analysis ◽  
Independent Variables ◽  
Equal Work ◽  
Maximum Work ◽  
Cycle Temperature ◽  
Selection Of

The thermal efficiency, work per unit mass, and work per unit volume of the simple Rankine and Brayton cycles are expressed in terms of seven independent variables using a simplified thermodynamic model. By requiring equal efficiency, equal work conditions, and the same maximum cycle temperature for both cycles, two necessary relationships are established between the seven independent variables. These two relationships along with two maximum work conditions produce a method for comparing required and selected properties. These comparisons provide useful guidelines for the selection of the cycle and cycle fluids. The comparison analysis shows that for a given application the more attractive cycle is strongly dependent upon the fluids selected.

scholarly journals A Preconditioned Iteration Method for Solving Sylvester Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Jituan Zhou ◽  
Ruirui Wang ◽  
Qiang Niu
Keyword(s):  
Iterative Method ◽  
Iteration Method ◽  
Linear Equations ◽  
System Of Linear Equations ◽  
Newton's Iteration ◽  
Gradient Based ◽  
Selection Of

A preconditioned gradient-based iterative method is derived by judicious selection of two auxil- iary matrices. The strategy is based on the Newton’s iteration method and can be regarded as a generalization of the splitting iterative method for system of linear equations. We analyze the convergence of the method and illustrate that the approach is able to considerably accelerate the convergence of the gradient-based iterative method.

scholarly journals EM Estimation of the X-Ray Spectrum With a Genetically Optimized Step-Wedge Phantom

2021 ◽  
Vol 9 ◽  
Author(s):  
Mengzhou Li ◽  
Feng-Lei Fan ◽  
Wenxiang Cong ◽  
Ge Wang
Keyword(s):  
Energy Spectrum ◽  
Condition Number ◽  
Linear Equations ◽  
Spectrum Estimation ◽  
Genetic Optimization ◽  
System Matrix ◽  
X Ray ◽  
Phantom Design ◽  
Selection Of ◽  
Spectrum Inversion

The energy spectrum of an X-ray tube plays an important role in computed tomography (CT), and is often estimated from physical measurement of dedicated phantoms. Usually, this estimation problem is reduced to solving a system of linear equations, which is generally ill-conditioned. In this paper, we optimize a phantom design to find the most effective combinations of thicknesses for different materials. First, we analyze the ill-posedness of the energy spectrum inversion when the number of unknown variables (N) and measurements (M) are equal, and show the condition number of the system matrix increases exponentially with N if the transmission thicknesses are linearly changed. Then, we present a genetic optimization algorithm to minimize the condition number of the system matrix in a general case (M < N) with respect to the selection of thicknesses and types of phantom materials. Finally, in the simulation with Poisson noise we study the accuracy of the spectrum estimation using the expectation-maximum algorithm. Our results indicate that the proposed method allows high-quality spectrum estimation, and the number of measurements is reduced over two thirds of that required by the widely-used method using a phantom with linearly-changed thicknesses.

The boundary layer over an impulsively started flat plate

1969 ◽  
Vol 310 (1502) ◽  
pp. 401-414 ◽  
Keyword(s):  
Boundary Layer ◽  
Leading Edge ◽  
Surface Shear Stress ◽  
Unsteady State ◽  
Similarity Condition ◽  
Surface Shear ◽  
Boundary Layer Problem ◽  
Independent Variables ◽  
Selection Of ◽  
Layer Problem

A numerical solution has been obtained for the development of the flow from the initial unsteady state described by Rayleigh to the ultimate steady state described by Blasius. The usual formulation of the problem in two independent variables is dropped, and three independent variables, in space and time, are reverted to. The boundary-layer problem is unconventional in that the boundary conditions are not completely known. Instead, it is known that the solution should satisfy a similarity condition, and use is made of this to obtain a solution by iteration. A finite-difference technique of a mixed, explicit-implicit, type is employed. The iteration converges rapidly. It is terminated where the maximum errors are estimated to be about 0.04%. A selection of the results for the velocity profiles and the surface shear stress is presented. One striking feature is the rapidity of the transition from the Rayleigh to the Blasius state. The change is practically complete, at a given station on the plate, by the time the plate has moved a distance equal to four times the distance from the station to the leading edge of the plate.

Comparison of Personality Characteristics of Physical Education and Recreation Majors, and Factors Which Affect Career Choice

1980 ◽  
Vol 51 (3_suppl2) ◽  
pp. 1291-1298
Author(s):  
James A. Batesky ◽  
John A. Malacos ◽  
Kevin M. Purcell
Keyword(s):  
Physical Education ◽  
Personality Characteristics ◽  
Control Group ◽  
Directed Search ◽  
Education Majors ◽  
Personality Profiles ◽  
Education Professionals ◽  
Independent Variables ◽  
Physical Education Majors ◽  
Selection Of

This study examined the personality characteristics of physical education and recreation majors, and ascertained why some students choose one over the other. Forty-nine physical education and recreation majors were administered Holland's Self-directed Search. A 2 × 3 fixed-factorial design was employed, sex and major plus a control group were independent variables. Both 24 recreation and 25 physical education majors were alike in the personality profiles and were very similar to recreation and physical education professionals already in the field. Significant differences were found on secondary, less dominant characteristics which may contribute to selection of a specialization area.

scholarly journals On the differential equations of H. Lewy

1961 ◽  
Vol 2 (1) ◽  
pp. 11-16
Author(s):  
W. B. Smith-White
Keyword(s):  
Differential Equations ◽  
Special Form ◽  
Linear Equations ◽  
Systems Of Equations ◽  
Independent Variables ◽  
Image Position ◽  
Two Independent Variables

It is known that the theory of Cauchy's problem for differential equations with two independent variables is réducible to the corresponding problem for systems of quasi-linear equations. The reduction is carried further, by means of the theory of characteristics, to the case of systems of equations of the special form first considered by H. Lewy [1]. The simplest case is that of the pair of equationswhere the aii depend on z1 and z2. The problem to be considered is that of finding functions z1(x, y), z2(x, y) which satisfy (1) and which take prescribed values on x + y = 0.

Are the systems the same?

2020 ◽  
Vol 17 (1) ◽  
pp. 58-83
Author(s):  
Matthew Kanwit ◽  
Silvia Pisabarro Sarrió
Keyword(s):  
Comparative Method ◽  
Independent Variables ◽  
Languages In Contact ◽  
Preference Task ◽  
Selection Of

Abstract Although two languages in contact may contain similar structures, superficial structural similarities may abscond important differences. The comparative method critically determines whether the languages differ in relative rates of variant use, the significance of independent variables, constraint rankings, and ordering within factor groups (Poplack & Tagliamonte 2001). The study explored intensifier (i.e., degree modifier) variation between Spanish muy and bien and Catalan molt and ben “very”, as based on 84 sets of responses from bilinguals on a 24-item contextualized preference task (40 in Catalan, 44 in Spanish). Results indicated significantly higher selection of muy in Spanish than molt in Catalan. Moreover, independent variables played a greater role in Spanish, with adjective quality, animacy, and verb type all predicting intensifier selection, whereas in Catalan only adjective quality was predictive. The study provided the first variationist analysis of Catalan intensification, while also revealing key systemic differences between the two languages despite surface similarities.

scholarly journals Soft Sensor Application in Identification of the Activated Sludge Bulking Considering the Technological and Economical Aspects of Smart Systems Functioning

Sensors ◽  
2020 ◽  
Vol 20 (7) ◽  
pp. 1941 ◽  
Author(s):  
Bartosz Szeląg ◽  
Jakub Drewnowski ◽  
Grzegorz Łagód ◽  
Dariusz Majerek ◽  
Ewa Dacewicz ◽  
...  
Keyword(s):  
Activated Sludge ◽  
Smart Cities ◽  
Treatment Plant ◽  
Soft Sensor ◽  
Support Vector ◽  
Optimal Method ◽  
Independent Variables ◽  
Sludge Bulking ◽  
Selection Of

The paper presented the methodology for the construction of a soft sensor used for activated sludge bulking identification. Devising such solutions fits within the current trends and development of a smart system and infrastructure within smart cities. In order to optimize the selection of the data-mining method depending on the data collected within a wastewater treatment plant (WWTP), a number of methods were considered, including: artificial neural networks, support vector machines, random forests, boosted trees, and logistic regression. The analysis conducted sought the combinations of independent variables for which the devised soft sensor is characterized with high accuracy and at a relatively low cost of determination. With the measurement results pertaining to the quantity and quality of wastewater as well as the temperature in the activated sludge chambers, a good fit can be achieved with the boosted trees method. In order to simplify the selection of an optimal method for the identification of activated sludge bulking depending on the model requirements and the data collected within the WWTP, an original system of weight estimation was proposed, enabling a reduction in the number of independent variables in a model—quantity and quality of wastewater, operational parameters, and the cost of conducting measurements.

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