An extension of golden section algorithm for n-variable functions with MATLAB code

Rani, G. Sandhya; Jayan, Sarada; Nagaraja, K.V.

doi:10.1088/1757-899x/577/1/012175

Cited by 10 publications

(7 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is noted that the base flow, the deep blue curve with circles, is separated from the observation by means of a straight line. Table 2 lists the estimated parameters of two lag and route models presented in Tab 1, in which the values in parenthesis of the third column come from the multi-dimension golden section search method recently suggested by [44]. In fact, the golden section searc method has been originally developed to solve the one-dimensional search problem therefore, we estimate 𝐾 (the value in the second column of Table 2) for the lag and rou version of a linear reservoir model with the same 𝑇 , such as the one used in the storag 1, in which the values in parenthesis of the third column come from the multi-dimensional golden section search method recently suggested by [44].…”

Section: Resultsmentioning

confidence: 99%

Fractional Linear Reservoir Model as Elementary Hydrologic Response Function

Yoon,

Kim

2023

Water

View full text Add to dashboard Cite

This paper presents a fractional linear reservoir model as the elementary response function of hydrologic systems corresponding to the classical linear reservoir model and tests its applicability to rainfall–runoff modeling. To this end, we formulate a fractional linear reservoir model in terms of fractional calculus following the same procedure as the classical linear reservoir model and, at the simplest level, compare its performance of rainfall–runoff modeling with the linear and nonlinear reservoir models. The impulse response function of a fractional linear reservoir model, a probability density function (PDF) following the Mittag–Leffler distribution, shows nonlinearity due to its time-variant behavior compared to that of a linear reservoir model. In traditional linear hydrologic system theory, the lag and route version of a fractional linear reservoir model produces the fast-rising and slow-recession of runoff hydrographs, implying the mixed response of linear and nonlinear reservoir models to rainfall. So, a fractional linear reservoir model could be considered a fundamental tool to effectively reflect the nonlinearity of rainfall–runoff phenomena within the framework of the linear hydrologic system theory. In this respect, the fractional order of the storage relationship specifying a fractional linear reservoir model can be viewed as a kind of parameter to quantify the heterogeneity of runoff generation within a river basin.

show abstract

Section: Resultsmentioning

confidence: 99%

Fractional Linear Reservoir Model as Elementary Hydrologic Response Function

Yoon,

Kim

2023

Water

View full text Add to dashboard Cite

show abstract

“…GSS is one of the fastest direct search algorithms [23] to find the minimum or maximum value of a function. For the PHIL applications, GSS is to find the minimum of a function.…”

Section: B Iteration Methodsmentioning

confidence: 99%

New Power Interface Based on Multi-Dimensional Golden Section Search Algorithm for Power-Hardware-in-the-Loop Applications

Constantine,

Lian,

Fan

et al. 2024

IEEE Access

View full text Add to dashboard Cite

Power-Hardware-in-the-Loop (PHIL) is a kind of real-time simulation, capable of exchanging not just low-voltage, low current signals, but the power required by the power device under test (PDuT). PHIL requires a PDuT to be connected to a real-time digital power network simulator via a power interface (PI). There have been quite a few PIs proposed in the past. Among them, ideal transformer model (ITM) is the most commonly used due to its ease of implementation. Other PIs such as partial circuit duplication and damping impedance can be considered as an extended version of ITM. These PIs need to follow a strict impedance ratio between PDuT and the rest of the system prior to the PHIL implementation, which could be a tedious and difficult task. This paper proposed a new PI for PHIL based on multi-dimensional golden section search algorithm, which can eliminate such a constraint. The proposed method has been shown to have wider stability regions when PDuT is a passive device or active one such as an inverter based resource. Moreover, dynamic responses of the proposed method are similar to those of the ITM under stable conditions. The validity of the proposed method has been justified with offline simulation and experimental PHIL setups.INDEX TERMS Real-Time Simulation, Power Hardware-in-the-Loop (PHIL), Golden Section Search (GSS), Gauss-Seidel, Power Amplifier.

show abstract

“…(iii) Apply the twodimensional GSSA (2D GSSA) to Equation (36). With regard to the two-dimensional golden section search algorithm, one may refer to [43]. Remark 3.…”

Section: A Simple Methods For Nonlinear Eigenvalue Problemsmentioning

confidence: 99%

Regularized Normalization Methods for Solving Linear and Nonlinear Eigenvalue Problems

Liu,

Kuo,

Chang

2023

Mathematics

View full text Add to dashboard Cite

To solve linear and nonlinear eigenvalue problems, we develop a simple method by directly solving a nonhomogeneous system obtained by supplementing a normalization condition on the eigen-equation for the uniqueness of the eigenvector. The novelty of the present paper is that we transform the original homogeneous eigen-equation to a nonhomogeneous eigen-equation by a normalization technique and the introduction of a simple merit function, the minimum of which leads to a precise eigenvalue. For complex eigenvalue problems, two normalization equations are derived utilizing two different normalization conditions. The golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues, and simultaneously, we can obtain precise eigenvectors to satisfy the eigen-equation. Two regularized normalization methods can accelerate the convergence speed for two extensions of the simple method, and a derivative-free fixed-point Newton iterative scheme is developed to compute real eigenvalues, the convergence speed of which is ten times faster than the golden section search algorithm. Newton methods are developed for solving two systems of nonlinear regularized equations, and the efficiency and accuracy are significantly improved. Over ten examples demonstrate the high performance of the proposed methods. Among them, the two regularization methods are better than the simple method.

show abstract

An extension of golden section algorithm for n-variable functions with MATLAB code

Cited by 10 publications

References 12 publications

Fractional Linear Reservoir Model as Elementary Hydrologic Response Function

Fractional Linear Reservoir Model as Elementary Hydrologic Response Function

New Power Interface Based on Multi-Dimensional Golden Section Search Algorithm for Power-Hardware-in-the-Loop Applications

Regularized Normalization Methods for Solving Linear and Nonlinear Eigenvalue Problems

Contact Info

Product

Resources

About