Complexity of approximation with relative error criterion in worst, average, and probabilistic settings

SUMMARYIn this paper, the problem of real-time computation of a dynamic model of manipulator is considered. In order to decrease the number of operations for dynamic model computation, an approximate model is introduced. Also, a relative error criterion is proposed, which enables one to determine the computing periods of various parts of a dynamic model of manipulator.

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The Linear and Asymptotically Superlinear Convergence Rates of the Augmented Lagrangian Method with a Practical Relative Error Criterion

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595920400011 ◽

2020 ◽

Vol 37 (04) ◽

pp. 2040001

Author(s):

Xin-Yuan Zhao ◽

Liang Chen

Keyword(s):

Convergence Rate ◽

Rate Of Convergence ◽

Relative Error ◽

Superlinear Convergence ◽

Augmented Lagrangian ◽

Augmented Lagrangian Method ◽

Penalty Parameter ◽

Error Criterion ◽

Linear Rate ◽

Relative Error Criterion

In this paper, we conduct a convergence rate analysis of the augmented Lagrangian method with a practical relative error criterion designed in Eckstein and Silva [Mathematical Programming, 141, 319–348 (2013)] for convex nonlinear programming problems. We show that under a mild local error bound condition, this method admits locally a Q-linear rate of convergence. More importantly, we show that the modulus of the convergence rate is inversely proportional to the penalty parameter. That is, an asymptotically superlinear convergence is obtained if the penalty parameter used in the algorithm is increasing to infinity, or an arbitrarily Q-linear rate of convergence can be guaranteed if the penalty parameter is fixed but it is sufficiently large. Besides, as a byproduct, the convergence, as well as the convergence rate, of the distance from the primal sequence to the solution set of the problem is obtained.

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Optimization of radar scanning strategies using an ensemble relative error criterion

Applied Mathematics and Computation ◽

10.1016/j.amc.2006.10.054 ◽

2007 ◽

Vol 188 (1) ◽

pp. 693-712

Author(s):

Luther White ◽

Alan Shapiro

Keyword(s):

Relative Error ◽

Error Criterion ◽

Relative Error Criterion ◽

Scanning Strategies

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Application of pyrometer and standard sample to determine surface temperature of studied materials

Izmeritel`naya Tekhnika ◽

10.32446/0368-1025it.2019-12-9-13 ◽

2019 ◽

pp. 9-13

Author(s):

V.Ya. Mendeleyev ◽

V.A. Petrov ◽

A.V. Yashin ◽

A.I. Vangonen ◽

O.K. Taganov

Keyword(s):

Composite Material ◽

Surface Temperature ◽

Relative Error ◽

Wavelength Range ◽

Standard Sample ◽

A Priori ◽

Temperature Changes ◽

Surface Temperatures ◽

Relative Errors ◽

Normal Emissivity

Determining the surface temperature of materials with unknown emissivity is studied. A method for determining the surface temperature using a standard sample of average spectral normal emissivity in the wavelength range of 1,65–1,80 μm and an industrially produced Metis M322 pyrometer operating in the same wavelength range. The surface temperature of studied samples of the composite material and platinum was determined experimentally from the temperature of a standard sample located on the studied surfaces. The relative error in determining the surface temperature of the studied materials, introduced by the proposed method, was calculated taking into account the temperatures of the platinum and the composite material, determined from the temperature of the standard sample located on the studied surfaces, and from the temperature of the studied surfaces in the absence of the standard sample. The relative errors thus obtained did not exceed 1,7 % for the composite material and 0,5% for the platinum at surface temperatures of about 973 K. It was also found that: the inaccuracy of a priori data on the emissivity of the standard sample in the range (–0,01; 0,01) relative to the average emissivity increases the relative error in determining the temperature of the composite material by 0,68 %, and the installation of a standard sample on the studied materials leads to temperature changes on the periphery of the surface not exceeding 0,47 % for composite material and 0,05 % for platinum.

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Performance analysis of global local mean square error criterion of stochastic linearization for nonlinear oscillator

Vietnam Journal of Mechanics ◽

10.15625/0866-7136/12015 ◽

2019 ◽

Author(s):

Nguyen Cao Thang ◽

Luu Xuan Hung

Keyword(s):

Performance Analysis ◽

Mean Square Error ◽

Nonlinear Oscillators ◽

Degree Of Freedom ◽

Equivalent Linearization ◽

Mean Square ◽

Error Criterion ◽

Stochastic Linearization ◽

Local Mean ◽

Mean Square Error Criterion

The paper presents a performance analysis of global-local mean square error criterion of stochastic linearization for some nonlinear oscillators. This criterion of stochastic linearization for nonlinear oscillators bases on dual conception to the local mean square error criterion (LOMSEC). The algorithm is generally built to multi degree of freedom (MDOF) nonlinear oscillators. Then, the performance analysis is carried out for two applications which comprise a rolling ship oscillation and two degree of freedom one. The improvement on accuracy of the proposed criterion has been shown in comparison with the conventional Gaussian equivalent linearization (GEL).

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Error-aware Design Procedure to Implement Energy-efficient Approximate Squaring Hardware

Nanoscience &Nanotechnology-Asia ◽

10.2174/2210681209666190807143557 ◽

2020 ◽

Vol 10 (4) ◽

pp. 471-477

Author(s):

Merin Loukrakpam ◽

Ch. Lison Singh ◽

Madhuchhanda Choudhury

Keyword(s):

Energy Saving ◽

Relative Error ◽

Energy Efficient ◽

Piecewise Linear ◽

Arithmetic Operation ◽

Design Procedure ◽

Digital Signal ◽

Maximum Relative Error ◽

Square Function ◽

Efficient Design

Background:: In recent years, there has been a high demand for executing digital signal processing and machine learning applications on energy-constrained devices. Squaring is a vital arithmetic operation used in such applications. Hence, improving the energy efficiency of squaring is crucial. Objective:: In this paper, a novel approximation method based on piecewise linear segmentation of the square function is proposed. Methods: Two-segment, four-segment and eight-segment accurate and energy-efficient 32-bit approximate designs for squaring were implemented using this method. The proposed 2-segment approximate squaring hardware showed 12.5% maximum relative error and delivered up to 55.6% energy saving when compared with state-of-the-art approximate multipliers used for squaring. Results: The proposed 4-segment hardware achieved a maximum relative error of 3.13% with up to 46.5% energy saving. Conclusion:: The proposed 8-segment design emerged as the most accurate squaring hardware with a maximum relative error of 0.78%. The comparison also revealed that the 8-segment design is the most efficient design in terms of error-area-delay-power product.

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