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About 5,123 papers for “Piecewise linear function”
Žiga Pušnik (18806074), Miha Mraz (5093906), Nikolaj Zimic (18806077) et al. · Figshare · 2024
<p>Visualization of the loss function that describes the difference between the observed () and the expected (<i>x</i>) network density.</p>
Cited by 0Open access
R. Koch, C.R. Paul · Electronics Letters · 1973
A new method of representing a signal using piecewise-linear basis functions has been described. The letter provides a very simple method of determining the expansion coefficients as linear combinations of samples of the signal.
Cited by 0
Zeraoulia Elhadj, J. C. Sprott · Nonlinear oscillations · 2011
Cited by 3
Anatoliy Manov, В. П. Заставный · Expositiones Mathematicae · 2016
Cited by 5
Manuel Delgado‐Restituto, J. Ceballos‐Cáceres, Á. Rodríguez‐Vázquez · 2002
We present a systematic design technique for current-mode piecewise-linear (PWL) function generators. It uses two building blocks: a high-resolution current rectifier, and a programmable current amplifier. We show how to arrange these blocks to obtain basic non-linearities from which generic characteristics are built through aggregations. Measurements from a 1.0 /spl mu/m CMOS prototype chip show 10 pA resolution in the rectification operation and 0.6% non-linearity errors in the programmable scaling operation for 2 /spl mu/A input current range.
Cited by 3
Steffen Rebennack, Vitaliy Krasko · INFORMS journal on computing · 2019
Piecewise linear (PWL) functions are used in a variety of applications. Computing such continuous PWL functions, however, is a challenging task. Software packages and the literature on PWL function fitting are dominated by heuristic methods. This is true for both fitting discrete data points and continuous univariate functions. The only exact methods rely on nonconvex model formulations. Exact methods compute continuous PWL function for a fixed number of breakpoints minimizing some distance function between the original function and the PWL function. An optimal PWL function can only be computed if the breakpoints are allowed to be placed freely and are not fixed to a set of candidate breakpoints. In this paper, we propose the first convex model for optimal continuous univariate PWL function fitting. Dependent on the metrics chosen, the resulting formulations are either mixed-integer linear programming or mixed-integer quadratic programming problems. These models yield optimal continuous PWL functions for a set of discrete data. On the basis of these convex formulations, we further develop an exact algorithm to fit continuous univariate functions. Computational results for benchmark instances from the literature demonstrate the superiority of the proposed convex models compared with state-of-the-art nonconvex models.
Cited by 54
Fengjie Fu (7314347), Hongzhao Dong (7314350) · Figshare · 2019
Cited by 0Open access
Zrilic, Djuro, Ramirez, Jaime, Yuan, Bo et al. · NASA Technical Reports Server (NASA)
In this paper a simple, inexpensive, membership function circuit for fuzzy controllers is presented. The proposed circuit may be used to generate a general trapezoidal membership function. The slope and horizontal shift are fully programmable parameters.
Cited by 0Open access
Chengtao Wen, Xiaoyan Ma · IEEE Transactions on Circuits and Systems I Regular Papers · 2008
This paper proposes a basis-function canonical piecewise-linear (BF-CPWL) function, which can approximate any continuous function using a weighted sum of PWL BFs. The BF-CPWL approximation integrates Breiman's hinging hyperplane model and Julian's high-level canonical PWL approximation into a common theoretical framework. Moreover, an approximation algorithm is developed, which fits and adds the PWL BFs iteratively using a modified Gauss-Newton method. This algorithm guarantees a local convergence, while achieving a good tradeoff between computational simplicity and approximation accuracy. The BF-CPWL approximation can find applications in nonlinear circuit synthesis, dynamic system identification and control.
Cited by 15
Nicolás Rodríguez, P. Julián, Eduardo E. Paolini · 2019
Symmetric Simplicial (SS) PWL functions can be used to implement nonlinear functions with high power and area efficiency in VLSI architectures. However, they have a representation limitation, since they can only implement symmetric functions. In this paper we propose a method to achieve generic piecewise-linear (PWL) functions in an efficient way, no limited to symmetrical functions, by using a combination of Symmetric Simplicial (SS) PWL functions. We present preliminary results in 2 and 3-dimensional domains.
Cited by 2
Shenglan Ben, Jiansheng Chen, Guangda Su · 2009
Instead of constructing a complex aging model on the whole age space, a piecewise linear aging function is proposed to approximate the ground truth aging function locally. To handle the `regression toward the mean' problem of local aging function regression, a weighting strategy is used to assign larger weights to the samples near typical aging appearance of each age. In age estimation step, a global aging function is used to predict the test sample's rough age range and the local linear aging function on that range is then used to give a final result. Experimental results show that our method can get more accuracy results in facial age estimation.
Cited by 2
Yankun Jiang · Oxford University Research Archive (ORA) (University of Oxford) · 2009
In this paper the optimal decision to sell a stock in a given time is investigated when the drift term in Black Scholes setting is a piecewise linear function of time. The goal is to minimize the expected relative error between the discounted selling price and the discounted maximum price over a given time horizon. With the drift changing to a piecewise linear function, we are interested in that if the trend of the stock price changes during the same time horizon, and what would be the impact on the selling strategy. Keywords: piecewise linear drift function, optimal stopping time, value function, selling region, holding region
Cited by 0Open access
Dr. Lorenzo, Matteo Bianchi · Zenodo (CERN European Organization for Nuclear Research) · 2025
This paper explores a broader class of piecewise linear functions, extending their applicability beyond conventional domains. Piecewise linear functions are typically defined on closed convex domains, but this work introduces a more versatile set of maps known as SW(E m ,T). These maps are linear only on selected subsets of vectors and components, making them suitable for a wider range of applications.The paper establishes an exponential function, F, which maps linear spaces to the set SW(E m ,T). It rigorously proves the uniqueness and existence of a universal element, denoted as *, within this framework. Furthermore, the paper introduces r-subset wise linear skew symmetric maps denoted as Φ = ∑ λμνϕ, demonstrating that they can be fully characterized by their values for λμν and a basis of E.The concept of an r-determinant function is introduced, defined as an r-subset wise linear skew symmetric map Φ: E m → Γ, with Γ being an arbitrary field of characteristic 0. The paper delves into various properties of r-determinant maps, shedding light on their characteristics and utility.Additionally, the paper explores the adjoint of a linear map ψ ∈ L(E,F), where E and F represent linear spaces. It also discusses the development of an r-determinant function using r-cofactors.Furthermore, this work defines extensions of differential forms through r-subset wise skew symmetric maps, paving the way for generalized differential forms. The paper investigates the basis and spaces of these generalized differential forms.
Cited by 0Open access
櫻井智章, 室伏俊明 · Tokyo Tech Research Repository (Tokyo Institute of Technology) · 2006
Cited by 0
J. S. Frame · The Fibonacci quarterly · 1994
Cited by 0
Maria Laura Fois, Andrea Furcht · Rivista italiana di economia, demografia e statistica · 2025
We present here some preliminary results of an ongoing study. The subject of this work is the survival function composed of two distinct, but joined, linear segments, examined in a continuous context.
Cited by 0Open access
Noam Goldberg, Steffen Rebennack, Youngdae Kim et al. · Computational Optimization and Applications · 2021
Abstract We consider a nonconvex mixed-integer nonlinear programming (MINLP) model proposed by Goldberg et al. (Comput Optim Appl 58:523–541, 2014. 10.1007/s10589-014-9647-y ) for piecewise linear function fitting. We show that this MINLP model is incomplete and can result in a piecewise linear curve that is not the graph of a function, because it misses a set of necessary constraints. We provide two counterexamples to illustrate this effect, and propose three alternative models that correct this behavior. We investigate the theoretical relationship between these models and evaluate their computational performance.
Cited by 8Open access
Danny Z. Chen, Haitao Wang · Lecture notes in computer science · 2009
Cited by 20
Rudolf Dániel Prokaj, Peter Raith, Károly Simon · Proceedings of the American Mathematical Society · 2023
We consider iterated function systems on the real line that consist of continuous, piecewise linear functions. Under a mild separation condition, we show that the Hausdorff and box dimensions of the attractor are equal to the minimum of 1 and the exponent which comes from the most natural system of covers of the attractor.
Cited by 1
Pierre Dersin · 2023
Cited by 0