piecewise meaning: definition, etymology and quotations

piecewise

adv

Etymology From piece + -wise.

In terms or by means of pieces; a piece at a time.

Near-synonyms: piecemeal, apiece
One could even do the recount piecewise, starting with the most questionable regions.2006 August 13, “LETTERS; Practical Method for Mexican Vote Recount”, in Los Angeles Times:

Mathematics, Sciences Especially Throughout separate parts, but not necessarily throughout the whole.

automatic reconstruction of accurate, concise, piecewise smooth surface models from scattered range data1994 July 24, Hugues Hoppe, Tony DeRose, Tom Duchamp, Mark Halstead, Hubert Jin, John McDonald, Jean Schweitzer, Werner Stuetzle, “Piecewise smooth surface reconstruction”, in Proceedings of the 21st annual conference on Computer graphics and interactive techniques (SIGGRAPH '94), New York, NY, USA: Association for Computing Machinery, →DOI, →ISBN, pages 295–302:
theory of piecewise differentiable functions and, specifically, piecewise differentiable equations2012, Stefan Scholtes, Introduction to Piecewise Differentiable Equations (SpringerBriefs in Optimization), New York: Springer, →ISBN:

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piecewise linear model which can serve as the base of any other2013 March 9, Domine Leenaerts, Wim M. G. van Bokhoven, Piecewise Linear Modeling and Analysis, Springer Science & Business Media, →ISBN:

Derived terms: piecewise function, piecewise linear, piecewiseness, piecewise smooth

adj

Etymology From piece + -wise.

Mathematics, Sciences Defined by subfunctions and subdomains

Our formula is not defined as a piecewise function, but rather as a single closed-form expression2018 April 1, Ivan Matić, Radoš Radoičić, Dan Stefanica, “A sharp Pólya-based approximation to the normal cumulative distribution function”, in Applied Mathematics and Computation, volume 322, →DOI, →ISSN, pages 111–122:
is a piecewise function but not a PLQ function2019 September 1, Deepak Kumar, Yves Lucet, “Computation of the Epsilon-Subdifferential of Convex Piecewise Linear-Quadratic Functions in Optimal Worst-Case Time”, in Set-Valued and Variational Analysis, volume 27, number 3, →DOI, →ISSN, pages 623–641:

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a piecewise function that consists of a single quadratic term and a constant term2022, Ethan T. Wang, “Efficient Quantum State Preparation for the Cauchy Distribution Based on Piecewise Arithmetic”, in IEEE Transactions on Quantum Engineering, volume 3, →DOI, →ISSN, pages 1–9:

Mathematics, Sciences Abbreviation, Clipping Clipping of piecewise linear.

In piecewise regression we replace the concept1970 September 23, Victor E. McZgee, Willard T. Carleton, “Piecewise Regression”, in Journal of the American Statistical Association, volume 65, number 331, →DOI, →ISSN, pages 1109–1124:
we can get arbitrarily close to any piecewise function with knot locations satisfying2000 July 23, J. Pittman, C.A. Murthy, “Fitting optimal piecewise linear functions using genetic algorithms”, in IEEE Transactions on Pattern Analysis and Machine Intelligence, volume 22, number 7, →DOI, pages 701–718:

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In essence, a piecewise function over an interval2016 November 23, Daniel Berjon, Guillermo Gallego, Carlos Cuevas, Francisco Moran, Narciso Garcia, “Optimal Piecewise Linear Function Approximation for GPU-Based Applications”, in IEEE Transactions on Cybernetics, volume 46, number 11, →DOI, →ISSN, pages 2584–2595: