Quantum Approximation Error on Some Sobolev Classes

2007 ◽  
Author(s):  
Peixin Ye
Keyword(s):  
Approximation Error ◽  
Sobolev Classes ◽  
Quantum Approximation

THE MODEL FOR MANAGING INVESTMENTS IN THE MOSCOW ENVIRONMENT BASED ON A POWER REGRESSION EQUATION

2020 ◽  
Vol 2 (7) ◽  
pp. 91-99
Author(s):  
E. V. KOSTYRIN ◽  
◽  
M. S. SINODSKAYA ◽  
Keyword(s):  
Solid Waste ◽  
Influencing Factors ◽  
Pair Correlation ◽  
Approximation Error ◽  
Regression Equation ◽  
Regression Equations ◽  
The Impact ◽  
The Relationship ◽  
Average Approximation ◽  
Average Approximation Error

The article analyzes the impact of certain factors on the volume of investments in the environment. Regression equations describing the relationship between the volume of investment in the environment and each of the influencing factors are constructed, the coefficients of the Pearson pair correlation between the dependent variable and the influencing factors, as well as pairwise between the influencing factors, are calculated. The average approximation error for each regression equation is determined. A correlation matrix is constructed and a conclusion is made. The developed econometric model is implemented in the program of separate collection of municipal solid waste (MSW) in Moscow. The efficiency of the model of investment management in the environment is evaluated on the example of the growth of planned investments in the activities of companies specializing in the export and processing of solid waste.

POLYGONAL APPROXIMATION OF DIGITAL CURVE BASED ON REVERSE ENGINEERING CONCEPT

2013 ◽  
Vol 13 (04) ◽  
pp. 1350017 ◽  
Author(s):  
KUMAR S. RAY ◽  
BIMAL KUMAR RAY
Keyword(s):  
Reverse Engineering ◽  
Linear Time ◽  
Line Drawing ◽  
Approximation Error ◽  
Zero Approximation ◽  
Polygonal Approximation ◽  
Digital Curve ◽  
Symmetric Approximation ◽  
Engineering Concept ◽  
Automatic Algorithm

This paper applies reverse engineering on the Bresenham's line drawing algorithm [J. E. Bresenham, IBM System Journal, 4, 106–111 (1965)] for polygonal approximation of digital curve. The proposed method has a number of features, namely, it is sequential and runs in linear time, produces symmetric approximation from symmetric digital curve, is an automatic algorithm and the approximating polygon has the least non-zero approximation error as compared to other algorithms.

scholarly journals Two-stage segment linearization as part of the thermocouple measurement chain

2021 ◽  
Vol 54 (1-2) ◽  
pp. 141-151
Author(s):  
Dragan Živanović ◽  
Milan Simić
Keyword(s):  
Transfer Functions ◽  
Approximation Error ◽  
Linearization Method ◽  
Linear Segment ◽  
Virtual Instrumentation ◽  
Memory Consumption ◽  
Thermocouple Measurement ◽  
Two Stage ◽  
Approximation Errors ◽  
Input Range

An implementation of a two-stage piece-wise linearization method for reduction of the thermocouple approximation error is presented in the paper. First, the whole thermocouple measurement chain of a transducer is described, and possible error is analysed to define the required level of accuracy for linearization of the transfer characteristics. Evaluation of linearization functions and analysis of approximation errors are performed by the virtual instrumentation software package LabVIEW. The method is appropriate for thermocouples and other sensors where nonlinearity varies a lot over the range of input values. The basic principle of this method is to first transform the abscissa of the transfer function by a linear segment look-up table in such a way that significantly nonlinear parts of the input range are expanded before a standard piece-wise linearization. In this way, applying equal-segment linearization two times has a similar effect to non-equal-segment linearization. For a given examples of the thermocouple transfer functions, the suggested method provides significantly better reduction of the approximation error, than the standard segment linearization, with equal memory consumption for look-up tables. The simple software implementation of this two-stage linearization method allows it to be applied in low calculation power microcontroller measurement transducers, as a replacement of the standard piece-wise linear approximation method.

scholarly journals Algebraic Solution to Constrained Bi-Criteria Decision Problem of Rating Alternatives through Pairwise Comparisons

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 303
Author(s):  
Nikolai Krivulin
Keyword(s):  
Decision Problem ◽  
Optimization Problem ◽  
Pareto Frontier ◽  
Sufficient Conditions ◽  
Approximation Error ◽  
Optimal Solution ◽  
Algebraic Solution ◽  
Pairwise Comparisons ◽  
Logarithmic Scale ◽  
Idempotent Algebra

We consider a decision-making problem to evaluate absolute ratings of alternatives from the results of their pairwise comparisons according to two criteria, subject to constraints on the ratings. We formulate the problem as a bi-objective optimization problem of constrained matrix approximation in the Chebyshev sense in logarithmic scale. The problem is to approximate the pairwise comparison matrices for each criterion simultaneously by a common consistent matrix of unit rank, which determines the vector of ratings. We represent and solve the optimization problem in the framework of tropical (idempotent) algebra, which deals with the theory and applications of idempotent semirings and semifields. The solution involves the introduction of two parameters that represent the minimum values of approximation error for each matrix and thereby describe the Pareto frontier for the bi-objective problem. The optimization problem then reduces to a parametrized vector inequality. The necessary and sufficient conditions for solutions of the inequality serve to derive the Pareto frontier for the problem. All solutions of the inequality, which correspond to the Pareto frontier, are taken as a complete Pareto-optimal solution to the problem. We apply these results to the decision problem of interest and present illustrative examples.

scholarly journals Some algorithms for maximum volume and cross approximation of symmetric semidefinite matrices

2021 ◽  
Author(s):  
Stefano Massei
Keyword(s):  
Computer Science ◽  
Recent Work ◽  
Linear Algebra ◽  
Optimization Problems ◽  
Approximation Error ◽  
Positive Semidefinite ◽  
Numerical Linear Algebra ◽  
Maximum Volume ◽  
Deterministic Algorithms ◽  
Principal Submatrix

AbstractVarious applications in numerical linear algebra and computer science are related to selecting the $$r\times r$$ r × r submatrix of maximum volume contained in a given matrix $$A\in \mathbb R^{n\times n}$$ A ∈ R n × n . We propose a new greedy algorithm of cost $$\mathcal O(n)$$ O ( n ) , for the case A symmetric positive semidefinite (SPSD) and we discuss its extension to related optimization problems such as the maximum ratio of volumes. In the second part of the paper we prove that any SPSD matrix admits a cross approximation built on a principal submatrix whose approximation error is bounded by $$(r+1)$$ ( r + 1 ) times the error of the best rank r approximation in the nuclear norm. In the spirit of recent work by Cortinovis and Kressner we derive some deterministic algorithms, which are capable to retrieve a quasi optimal cross approximation with cost $$\mathcal O(n^3)$$ O ( n 3 ) .

scholarly journals On Hermite-Fejér type interpolation on the Chebyshev nodes

1993 ◽  
Vol 47 (1) ◽  
pp. 13-24 ◽  
Author(s):  
Graeme J. Byrne ◽  
T.M. Mills ◽  
Simon J. Smith
Keyword(s):  
Approximation Error ◽  
Interpolation Polynomial ◽  
Precise Estimate ◽  
Type Interpolation ◽  
Interpolation Methods ◽  
Chebyshev Nodes ◽  
Interpolatory Process

Given f ∈ C [−1, 1], let Hn, 3(f, x) denote the (0,1,2) Hermite-Fejér interpolation polynomial of f based on the Chebyshev nodes. In this paper we develop a precise estimate for the magnitude of the approximation error |Hn, 3(f, x) − f(x)|. Further, we demonstrate a method of combining the divergent Lagrange and (0,1,2) interpolation methods on the Chebyshev nodes to obtain a convergent rational interpolatory process.

Sign in / Sign up

Export Citation Format

Share Document