Transforming the canonical piecewise-linear model into a smooth-piecewise representation

被引：13

作者：

Jimenez-Fernandez, Victor M. ^{[1
]}

Jimenez-Fernandez, Maribel ^{[2
]}

Vazquez-Leal, Hector ^{[1
]}

Munoz-Aguirre, Evodio ^{[3
]}

Cerecedo-Nunez, Hector H. ^{[4
]}

Filobello-Nino, Uriel A. ^{[1
]}

Castro-Gonzalez, Francisco J. ^{[1
]}

机构：

[1] Univ Veracruzana, Zona Univ, Fac Elect Instrumentat, Circuito Gonzalo Aguirre Beltran S-N, Xalapa 91000, Veracruz, Mexico

[2] Univ Veracruzana, Inst Basic Sci, Av Castelazo Ayala S-N, Xalapa 91192, Veracruz, Mexico

[3] Univ Veracruzana, Zona Univ, Fac Math, Circuito Gonzalo Aguirre Beltran S-N, Xalapa 91000, Veracruz, Mexico

[4] Univ Veracruzana, Zona Univ, Fac Phys, Circuito Gonzalo Aguirre Beltran S-N, Xalapa 91000, Veracruz, Mexico

来源：

SPRINGERPLUS | 2016年 / 5卷

关键词：

Smooth; Canonical; Piecewise-linear; Model; EFFICIENT; ALGORITHM;

D O I：

10.1186/s40064-016-3278-y

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

A smoothed representation (based on natural exponential and logarithmic functions) for the canonical piecewise-linear model, is presented. The result is a completely differentiable formulation that exhibits interesting properties, like preserving the parameters of the original piecewise-linear model in such a way that they can be directly inherited to the smooth model in order to determine their parameters, the capability of controlling not only the smoothness grade, but also the approximation accuracy at specific breakpoint locations, a lower or equal overshooting for high order derivatives in comparison with other approaches, and the additional advantage of being expressed in a reduced mathematical form with only two types of inverse functions (logarithmic and exponential). By numerical simulation examples, this proposal is verified and well-illustrated.

引用

页数：17

共 29 条

[1] BACON DW, 1971, BIOMETRIKA, V58, P525, DOI 10.2307/2334387
[2] Using piecewise linear interpolations in spherical harmonic analysis
Bian, S
Menz, J
[J]. JOURNAL OF GEODESY, 1998, 72 (7-8) : 473 - 481
[3] Brooks, 2008, INTRO ECONOMETRICS F, P462
[4] UNIVERSAL NETWORK REALIZING BASIC PIECEWISE-LINEAR I/V CHARACTERISTICS
BRZOBOHATY, J
POSPISIL, J
[J]. ELECTRONICS LETTERS, 1991, 27 (05) : 402 - 404
[5] CANONICAL PIECEWISE-LINEAR MODELING
CHUA, LO
DENG, AC
[J]. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1986, 33 (05): : 511 - 525
[6] SECTION-WISE PIECEWISE-LINEAR FUNCTIONS - CANONICAL REPRESENTATION, PROPERTIES, AND APPLICATIONS
CHUA, LO
KANG, SM
[J]. PROCEEDINGS OF THE IEEE, 1977, 65 (06) : 915 - 929
[7] CANONICAL PIECEWISE-LINEAR ANALYSIS .2. TRACING DRIVING-POINT AND TRANSFER CHARACTERISTICS
CHUA, LO
DENG, AC
[J]. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1985, 32 (05): : 417 - 444
[8] CANONICAL PIECEWISE-LINEAR ANALYSIS
CHUA, LO
YING, RLP
[J]. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1983, 30 (03): : 125 - 140
[9] CANONICAL PIECEWISE-LINEAR REPRESENTATION
CHUA, LO
DENG, AC
[J]. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1988, 35 (01): : 101 - 111
[10] Dai TS, 2007, LECT NOTES COMPUT SC, V4508, P262

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