Investigating an overdetermined system of linear equations by using convex functions

Pavić, Zlatko; Novoselac, Vedran

doi:10.15672/hjms.2017.423

Cited by 3 publications

(2 citation statements)

References 9 publications

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“…According to (4) and ( 5), we draw the conclusion of the equations of α = A + e x and β = A + e y . Under the condition of over-determination, we gained that A + = (A A) −1 A , thereby calculating the values of α and β [25], [26], and completing the fitting of the error curved surface.…”

Section: B Error Curved Surface Interpolation Methodsmentioning

confidence: 99%

Position Measurement of Laser Center by Using 2-D PSD and Fixed-Axis Rotating Device

et al. 2019

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Photoelectric non-contact measurement methods have been widely implemented in space target location, micro-displacement measurement and space optical communication. In term of the reliability and precision of measurement systems, it is a great significance to obtain the laser center location accurately. Since the two-dimensional position sensitive detector (2-D PSD) can continuously detects the gravity center position of the laser spot on its photosensitive surface, this paper provides a flexible method with high precision for the nonlinear correction of PSD as well as a new idea for PSD-based moving laser center positioning. Above all, a laser device system that rotating around a fixed-axis is designed, and the rotation angle can be controlled with the rotation accuracy of 0.5 • . The trace of the gravity center of the rotating spot generated by the device on the PSD surface is detected, and then the laser center location is obtained after further processing of data. In order to improve the detection accuracy of PSD, this research mainly focuses on the nonlinear correction method of the detector and the fitting method of the gravity center trace of the laser spot. Moreover, the effects of different sizes of light spots projected onto the 2-D PSD on the collected photocurrent and estimated coordinates were analyzed by experiments. From the experimental results, the non-linear error of PSD is corrected by the error curved surface interpolation method, the overall error is reduced by more than 32%, and the linearity of the positioning of the laser moving along the diagonal of PSD is 0.2%.

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Section: B Error Curved Surface Interpolation Methodsmentioning

confidence: 99%

Position Measurement of Laser Center by Using 2-D PSD and Fixed-Axis Rotating Device

et al. 2019

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“…The paper [14] is concerned with the various sets of sufficient conditions for the existence and nonexistence of solutions to the Dirichlet boundary value problem. The paper [22] investigates the use of convex functions to demonstrate the existence of optimal solutions to an over-determined system of linear equations. The duality theorems demonstrated that a sufficient condition for an extremum is an extremal relation for both the primal and dual problems.…”

Section: Introductionmentioning

confidence: 99%

On duality in convex optimization of second-order differential inclusions with periodic boundary conditions

Sağlam

Mahmudov

2022

Hacettepe Journal of Mathematics and Statistics

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The present paper is devoted to the duality theory for the convex optimal control problem of second-order differential inclusions with periodic boundary conditions. First, we use an auxiliary problem with second-order discrete-approximate inclusions and focus on formulating sufficient conditions of optimality for the differential problem. Then, we concentrate on the duality that exists in periodic boundary conditions to establish a dual problem for the differential problem and prove that Euler-Lagrange inclusions are duality relations for both primal and dual problems. Finally, we consider an example of the duality for the second-order linear optimal control problem.

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Online prediction of network-level public transport demand based on principle component analysis

Zhong¹,

Wu²,

Zhang³

et al. 2023

Communications in Transportation Research

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Investigating an overdetermined system of linear equations by using convex functions

Cited by 3 publications

References 9 publications

Position Measurement of Laser Center by Using 2-D PSD and Fixed-Axis Rotating Device

Position Measurement of Laser Center by Using 2-D PSD and Fixed-Axis Rotating Device

On duality in convex optimization of second-order differential inclusions with periodic boundary conditions

Online prediction of network-level public transport demand based on principle component analysis

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