piecewise

English

Etymology

From piece +‎ -wise.

Adverb

piecewise (not comparable)

1. In terms or by means of pieces; a piece at a time.
   • 2006 August 13, “LETTERS; Practical Method for Mexican Vote Recount”, in Los Angeles Times:

     One could even do the recount piecewise, starting with the most questionable regions.

2. (mathematics) Throughout separate parts, but not necessarily throughout the whole
   • 1994 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)‎^[1], New York, NY, USA: Association for Computing Machinery, →DOI, →ISBN, pages 295–302:

     automatic reconstruction of accurate, concise, piecewise smooth surface models from scattered range data

   • 2012, Stefan Scholtes, Introduction to Piecewise Differentiable Equations (SpringerBriefs in Optimization), New York: Springer, →ISBN:

     theory of piecewise differentiable functions and, specifically, piecewise differentiable equations

   • 2013 March 9, Domine Leenaerts, Wim M. G. van Bokhoven, Piecewise Linear Modeling and Analysis‎^[2], Springer Science & Business Media, →ISBN:

     piecewise linear model which can serve as the base of any other

Derived terms

• piecewise linear
• piecewiseness

Translations

piece at a time

• Finnish: paloittain (fi)
• Swedish: stegvis (sv), steg för steg (sv), etappvis (sv)

mathematics: throughout separate parts but not necessarily throughout the whole

• Finnish: paloittain (fi)
• French: par morceaux
• Icelandic: á köflum (is)
• Japanese: 区分的に (くぶんてきに, kubunteki-ni)

Adjective

piecewise (comparative more piecewise, superlative most piecewise)

2. (mathematics) Defined by subfunctions and subdomains

   Synonym: piecewise-defined

   • 2018 April 1, Ivan Matić, Radoš Radoičić, Dan Stefanica, “A sharp Pólya-based approximation to the normal cumulative distribution function”, in Applied Mathematics and Computation‎^[3], volume 322, →DOI, →ISSN, pages 111–122:

     Our formula is not defined as a piecewise function, but rather as a single closed-form expression

   • 2019 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^[4], volume 27, number 3, →DOI, →ISSN, pages 623–641:

     is a piecewise function but not a PLQ function

   • 2022, Ethan T. Wang, “Efficient Quantum State Preparation for the Cauchy Distribution Based on Piecewise Arithmetic”, in IEEE Transactions on Quantum Engineering‎^[5], volume 3, →DOI, →ISSN, pages 1–9:

     a piecewise function that consists of a single quadratic term and a constant term

3. (mathematics) Clipping of piecewise linear.
   • 1970 September, Victor E. McZgee, Willard T. Carleton, “Piecewise Regression”, in Journal of the American Statistical Association‎^[6], volume 65, number 331, →DOI, →ISSN, pages 1109–1124:

     In piecewise regression we replace the concept

   • 2000 July, J. Pittman, C.A. Murthy, “Fitting optimal piecewise linear functions using genetic algorithms”, in IEEE Transactions on Pattern Analysis and Machine Intelligence‎^[7], volume 22, number 7, →DOI, pages 701–718:

     we can get arbitrarily close to any piecewise function with knot locations satisfying

   • 2016 November, Daniel Berjon, Guillermo Gallego, Carlos Cuevas, Francisco Moran, Narciso Garcia, “Optimal Piecewise Linear Function Approximation for GPU-Based Applications”, in IEEE Transactions on Cybernetics‎^[8], volume 46, number 11, →DOI, →ISSN, pages 2584–2595:

     In essence, a piecewise function over an interval