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Topics referred to by the same term
Piecewise linear may refer to: Piecewise linear curve, a connected sequence of line segments Piecewise linear function, a function whose domain can be
Piecewise_linear
Type of mathematical function
piecewise linear or segmented function is a real-valued function of a real variable, whose graph is composed of straight-line segments. A piecewise linear
Piecewise_linear_function
Function defined by multiple sub-functions
as a piecewise function. The first three paragraphs of this article only deal with this first meaning of "piecewise". Terms like piecewise linear, piecewise
Piecewise_function
Method of curve fitting
for linear interpolation given above. Linear interpolation on a set of data points (x0, y0), (x1, y1), ..., (xn, yn) is defined as piecewise linear, resulting
Linear_interpolation
Topological manifold with a piecewise linear structure on it
In mathematics, a piecewise linear manifold (PL manifold) is a topological manifold together with a piecewise linear structure on it. Such a structure
Piecewise_linear_manifold
Numerical method for solving physical or engineering problems
On the other hand, some authors replace "piecewise linear" with "piecewise quadratic" or even "piecewise polynomial". The author might then say "higher
Finite_element_method
Representation of mathematical space
a triangulable space. Triangulations can also be used to define a piecewise linear structure for a space, if one exists. Triangulation has various applications
Triangulation_(topology)
Linear combination of indicator functions of real intervals
written as a finite linear combination of indicator functions of intervals. Informally speaking, a step function is a piecewise constant function having
Step_function
Type of activation function
context of artificial neural networks, the rectifier or ReLU (rectified linear unit) activation function is an activation function defined as the non-negative
Rectified_linear_unit
Connected series of line segments
polygonal path, polyline, piecewise linear curve, broken line or, in geographic information systems, a linestring or linear ring. Mehlhorn, Kurt; Näher
Polygonal_chain
Simplicial continuation, or piecewise linear continuation (Allgower and Georg), is a one-parameter continuation method which is well suited to small to
Piecewise_linear_continuation
Category of piecewise-smooth manifolds
smooth functions between them) and PL (the category of piecewise linear manifolds and piecewise linear maps between them), and the reason it is defined is
PDIFF
Assemblage of connected electrical elements
specialized computer programs or estimation techniques such as the piecewise-linear model. Circuit simulation software, such as HSPICE (an analog circuit
Electrical_network
Algorithm for generating pseudo-randomized numbers
A linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear
Linear_congruential_generator
Musical interval unit
to 1⁄12, the function 2x increases almost linearly from 1.00000 to 1.05946, allowing for a piecewise linear approximation. Thus, although cents represent
Cent_(music)
Linear map or polynomial function of degree one
Nonlinear system Piecewise linear function Linear approximation Linear interpolation Discontinuous linear map Linear least squares "The term linear function means
Linear_function
Mathematical model of the time dependence of a point in space
with just second-degree polynomials; the horseshoe map is piecewise linear. For non-linear autonomous ODEs it is possible under some conditions to develop
Dynamical_system
Determining all voltages and currents within an electrical network
been given at the top of this (non-linear) section. However, this formula is rarely used in network analysis, a piecewise approximation being used instead
Network analysis (electrical circuits)
Network_analysis_(electrical_circuits)
Exponent of a power of two
mantissa of approximately 0.44. It can be made more accurate by using a piecewise linear function of m {\displaystyle m} , or more crudely by adding a constant
Binary_logarithm
ring: The definition is similar to cobordism, except that one uses piecewise linear or topological instead of smooth manifolds, either oriented or unoriented
List_of_cohomology_theories
Model in digital signal processing
circuit called an integrator. For FOH, the signal is reconstructed as a piecewise linear approximation to the original signal that was sampled. A mathematical
First-order_hold
Statistical method of dividing data into equal-sized intervals for analysis
include: Notes: R‑1 through R‑3 are piecewise constant, with discontinuities. R‑4 and following are piecewise linear, without discontinuities, but differ
Quantile
Mathematical function conceived as a crude model
classification), but they may also take the form of other nonlinear functions, piecewise linear functions, or step functions. They are also often monotonically increasing
Artificial_neuron
Piece-wise division of objects
constant U. A piecewise-linear valuation is a generalization of piecewise-constant valuation in which the value-density in each region j is a linear function
Piecewise-constant_valuation
rising from 0 to 1, but using simpler functions, especially piecewise linear functions or piecewise constant functions. These are preferred where speed of
Hard_sigmoid
collapsible. Any n-dimensional PL manifold that is collapsible is in fact piecewise-linearly isomorphic to an n-ball. Discrete Morse theory – Combinatorial approach
Collapse_(topology)
named after Udo Pachner, are ways of replacing a triangulation of a piecewise linear manifold by a different triangulation of a homeomorphic manifold. Pachner
Pachner_moves
Computational statistics technique
with or, at least, closer to piecewise linear). Instead of a single uniform envelope density function, use a piecewise linear density function as your envelope
Rejection_sampling
Extends the Jordan curve theorem to characterize the inner and outer regions
first be proved for polygons when the homeomorphism can be taken to be piecewise linear and the identity map off some compact set; the case of a continuous
Schoenflies_problem
model was first introduced in a paper by Mark H. A. Davis in 1984. Piecewise linear models such as Markov chains, continuous-time Markov chains, the M/G/1
Piecewise-deterministic Markov process
Piecewise-deterministic_Markov_process
function f : | K | → | L | {\displaystyle f:|K|\to |L|} is called piecewise-linear (PL) if there exist a subdivision K' of K, and a subdivision L' of
Simplicial_map
Any mathematical model describing semiconductor diodes
diode is called piecewise linear (PWL) modelling. In mathematics, this means taking a function and breaking it down into several linear segments. This
Diode_modelling
Topics referred to by the same term
functions with such piecewise properties are: Piecewise constant function, also known as a step function Piecewise linear function Piecewise continuous function
Piecewise_property
Finite volume method in partial differential equations
use piecewise linear approximations of each cell, which results in a central difference scheme that is second-order accurate in space. The piecewise linear
MUSCL_scheme
Space-filling curve
Hausdorff dimension 1). The Hilbert curve is constructed as a limit of piecewise linear curves. The length of the n {\displaystyle n} th curve is 2 n − 1 2
Hilbert_curve
Theorem in geometric topology
suspension S2X of a homology sphere X is a topological sphere. If X is a piecewise-linear homology sphere but not a sphere, then its double suspension S2X (with
Double_suspension_theorem
Curve simplification algorithm
Simplifying a piecewise linear curve with the Douglas–Peucker algorithm.
Ramer–Douglas–Peucker algorithm
Ramer–Douglas–Peucker_algorithm
Non-sinusoidal waveform
considered the extreme case of an asymmetric triangle wave. The equivalent piecewise linear functions x ( t ) = t − ⌊ t ⌋ {\displaystyle x(t)=t-\lfloor t\rfloor
Sawtooth_wave
Piecewise-linear manifold
topology, a Kervaire manifold K 4 n + 2 {\displaystyle K^{4n+2}} is a piecewise-linear manifold of dimension 4 n + 2 {\displaystyle 4n+2} constructed by Michel
Kervaire_manifold
Computational problems no algorithm can solve
attraction of a given open set, in a piecewise-linear iterated map in two dimensions, or in a piecewise-linear flow in three dimensions. Finding the
List_of_undecidable_problems
Non-sinusoidal waveform
non-sinusoidal waveform named for its triangular shape. It is a periodic, piecewise linear, continuous real function. Like a square wave, the triangle wave contains
Triangle_wave
Any topological 3-manifold has unique PL and smooth structures
states that any topological 3-manifold has an essentially unique piecewise-linear structure and smooth structure. The analogue of Moise's theorem in
Moise's_theorem
Simulation software for electrical circuits
PLECS (Piecewise Linear Electrical Circuit Simulation) is a software tool for system-level simulations of electrical circuits developed by Plexim. It is
PLECS
temperature stability and other non-ideal effects. Piecewise linear functions can approximate non-linear functions as a series of connected line segments
Operational amplifier applications
Operational_amplifier_applications
Numerical method for differential equations
local linearization (LL) method is a general strategy for designing numerical integrators for differential equations based on a local (piecewise) linearization
Local_linearization_method
Pathological embedding of the sphere in 3D space
embeddings. This distinction led to the development of PL topology (Piecewise Linear) and eventually helped frame the Generalized Poincaré conjecture. The
Alexander_horned_sphere
Approximation to shape of a point cloud
computational geometry, an alpha shape, or α-shape, is a family of piecewise linear simple curves in the Euclidean plane associated with the shape of a
Alpha_shape
First known wavelet basis
t\in [0,1],\ 0\leq k<2^{n}.} These functions sn,k are continuous, piecewise linear, supported by the interval In,k that also supports ψn,k. The function
Haar_wavelet
Software product
electronic circuit simulator with ideal and piecewise-linear components. The first generation of NL (non-linear) analog simulator was developed in the late
NL5_circuit_simulator
Mathematical space
neighbourhood that is homeomorphic to Euclidean 3-space. The topological, piecewise-linear, and smooth categories are all equivalent in three dimensions, so little
3-manifold
first-order method, based on (piecewise) constant approximation Trapezoidal rule — second-order method, based on (piecewise) linear approximation Simpson's
List of numerical analysis topics
List_of_numerical_analysis_topics
Mathematical theory in topological dynamics
and finally published in 1988. Applications of the theory include piecewise linear models, counting of fixed points, computing the total variation, and
Milnor–Thurston kneading theory
Milnor–Thurston_kneading_theory
Array of numbers
systems. It attempts to approximate the solution to some equation by piecewise linear functions, where the pieces are chosen concerning a sufficiently fine
Matrix_(mathematics)
Theorem in topology
piecewise-linear map of a disk into a 3-manifold, with the map's singularity set in the disk's interior, implies the existence of another piecewise-linear
Dehn's_lemma
Tent function, often used in signal processing
and x j + 1 = 1 {\displaystyle x_{j+1}=1} . A linear B-spline is the same as a continuous piecewise linear function f ( x ) {\displaystyle f(x)} , and this
Triangular_function
Root-finding algorithm
then appears that I x {\displaystyle I_{x}} is a scaled and shifted piecewise-linear approximation of log 2 ( x ) {\displaystyle \log _{2}(x)} , as illustrated
Fast_inverse_square_root
Geometric theorem
paper left open the possibility that there exists a free group F of piecewise linear transformations acting on the punctured disk D \ {(0,0)} without fixed
Banach–Tarski_paradox
In mathematics, a partition of a manifold into submanifolds
are required to have a piecewise-linear, differentiable (of class Cr), or analytic structure then one defines piecewise-linear, differentiable, or analytic
Foliation
Matrix used in finite element analysis
e. piecewise linear basis functions on triangles, there are simple formulas for the element stiffness matrices. For example, for piecewise linear elements
Stiffness_matrix
Fundamental theorem in probability theory and statistics
realizations of the sum of n independent identical discrete variables, the piecewise-linear curve that joins the centers of the upper faces of the rectangles forming
Central_limit_theorem
Self-balancing binary search tree data structure
The graph of the function m h {\displaystyle m_{h}} is convex and piecewise linear with breakpoints at ( h = 2 k | m 2 k = 2 ⋅ 2 k − 2 ) {\displaystyle
Red–black_tree
Topological space that locally resembles Euclidean space
manifold which is discretization of a manifold. It usually means a piecewise linear manifold made by simplicial complexes. A digital manifold is a special
Manifold
Mathematical theories
concerned with when a topological manifold has a piecewise linear structure, and when a piecewise linear manifold has a differential structure. In dimension
Obstruction_theory
Software company
electronic systems. The company is known for its main product, PLECS (Piecewise Linear Electrical Circuit Simulation), which is used in the design and analysis
Plexim
Electronic resistor
two-terminal, nonlinear active resistor which can be described with piecewise-linear equations. It is an essential part of Chua's circuit, a simple electronic
Chua's_diode
Mathematical function defined piecewise by polynomials
In mathematics, a spline is a function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial
Spline_(mathematics)
Topics referred to by the same term
computer networking Digital Private Line, another form of tone squelching Piecewise linear (disambiguation), in mathematics Propositional logic, a system of evaluating
PL
Generalization of a Markov decision process
o)){\Bigr ]}} For finite-horizon POMDPs, the optimal value function is piecewise-linear and convex. It can be represented as a finite set of vectors. In the
Partially observable Markov decision process
Partially_observable_Markov_decision_process
Conservative numerical scheme
the physical input, for instance by replacing the piecewise constant approximation by a piecewise linear variation inside each cell, leading to the definition
Godunov's_scheme
British mathematician (1925–2016)
to mathematics were in topology, particularly in knot theory, the piecewise linear category, and dynamical systems. His 1955 thesis at the University
Christopher_Zeeman
Algorithm for measuring similarity between temporal sequences
sequences are "warped" non-linearly in the time dimension to determine a measure of their similarity independent of certain non-linear variations in the time
Dynamic_time_warping
Computational and mathematical modeling of complex biological systems
associated with network inference. Piecewise-linear differential equation models (PLDE): The model is composed of a piecewise-linear representation of differential
Systems_biology
Telecommunications and signal processing technique
In 1970, H. Kaneko developed the uniform description of segment (piecewise linear) companding laws that had by then been adopted in digital telephony
Companding
Hypothetical approach to quantum gravity with emergent spacetime
calculus where spacetime is discretized by approximating it with a piecewise linear manifold in a process called triangulation. In this process, a d-dimensional
Causal dynamical triangulation
Causal_dynamical_triangulation
Chaotic map
Gingerbreadman map is a chaotic two-dimensional map. It is given by the piecewise linear transformation: { x n + 1 = 1 − y n + | x n | y n + 1 = x n {\displaystyle
Gingerbreadman_map
Smooth manifold that is homeomorphic but not diffeomorphic to a sphere
theorem. (In contrast, in the piecewise linear setting the left-most map is onto via radial extension: every piecewise-linear-twisted sphere is standard
Exotic_sphere
Quality in crops
it the yield starts declining. The model is fitted to the data by piecewise linear regression. ^) Many variety names are uncommon as they consist of 3
Crop_tolerance_to_seawater
Free-surface modelling technique
SOLA-VOF code was also adopted by NASA. In 1982, Youngs developed the Piecewise-Linear Interface Calculation (PLIC) scheme, which improved accuracy of interface
Volume_of_fluid_method
Shape bounded by non-intersecting line segments
that does not intersect itself and has no holes. That is, it is a piecewise-linear Jordan curve consisting of finitely many line segments. These polygons
Simple_polygon
Method in numerical analysis
continuation must be used (see below). Simplicial Continuation, or Piecewise Linear Continuation (Allgower and Georg) is based on three basic results.
Numerical_continuation
Type of artificial neural network architecture
can capture both high-frequency and low-frequency data components. Piecewise linear functions: Provide efficient approximation for multivariate functions
Kolmogorov–Arnold_Networks
Topics referred to by the same term
Linear congruential generator (LCG), algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear equation
Linear_(disambiguation)
Regularization method for artificial neural networks
Bengio, Yoshua (2013-12-20). "An empirical analysis of dropout in piecewise linear networks". arXiv:1312.6197 [stat.ML]. Hinton, Geoffrey E.; Srivastava
Dropout_(neural_networks)
Non-parametric regression technique
creates the piecewise linear graph shown for the simple MARS model in the previous section. One might assume that only piecewise linear functions can
Multivariate adaptive regression spline
Multivariate_adaptive_regression_spline
Concept in statistical mathematics
Segmented regression, also known as piecewise regression or broken-stick regression, is a method in regression analysis in which the independent variable
Segmented_regression
Strong form of uniform continuity
metric on M or N. This structure is intermediate between that of a piecewise-linear manifold and a topological manifold: a PL structure gives rise to a
Lipschitz_continuity
Skeletonized version of algebraic geometry
variant of algebraic geometry in which polynomial graphs resemble piecewise linear meshes, and in which numbers belong to the tropical semiring instead
Tropical_geometry
Image luminance mapping function
counterproductive), because the floating-point format already provides a piecewise linear approximation of a logarithmic curve. Although gamma encoding was developed
Gamma_correction
Generalized function whose value is zero everywhere except at zero
total integral is 1). In some situations such as numerical analysis, a piecewise linear approximation to the identity is desirable. This can be obtained by
Dirac_delta_function
Family of second-order differential equations
existence of a limit cycle for such a system. A Liénard system with piecewise-linear functions can also contain homoclinic orbits. Let f and g be two continuously
Liénard_equation
Whether a manifold which is a homotopy sphere is a sphere
More precisely, one fixes a category of manifolds: topological (Top), piecewise linear (PL), or differentiable (Diff). Then the statement is Every homotopy
Generalized Poincaré conjecture
Generalized_Poincaré_conjecture
Function that is continuous everywhere but differentiable nowhere
example, the cosine function can be replaced in the infinite series by a piecewise linear "zigzag" function. G. H. Hardy showed that the function of the above
Weierstrass_function
January 2022. Synchronization of Chaotic Fractional-Order WINDMI Systems via Linear State Error Feedback Control Vaidyanathan, S.; Volos, Ch. K.; Rajagopal
List_of_chaotic_maps
Theorem in differential geometry
Descartes' theorem on total angular defect of a polyhedron is the piecewise-linear analog: it states that the sum of the defect at all the vertices of
Gauss–Bonnet_theorem
Models replicating electronic behavior
used mainly for power electronics represent piecewise linear algorithms. These algorithms use an analog (linear) simulation until a power electronic switch
Electronic_circuit_simulation
Electronic circuit that behaves chaotically
circuit containing a nonlinear element such that f(x) was a 3-segment piecewise-linear function. The easy experimental implementation of the circuit, combined
Chua's_circuit
of a model tree: a decision tree that has linear regression models at its leaves to provide a piecewise linear regression model (where ordinary decision
Logistic_model_tree
Fraction with denominator a power of two
unstable points in the parameter space of the Hénon map. The set of piecewise linear homeomorphisms from the unit interval to itself that have power-of-2
Dyadic_rational
Branch of topology
neighbourhood that is homeomorphic to Euclidean 3-space. The topological, piecewise-linear, and smooth categories are all equivalent in three dimensions, so little
Low-dimensional_topology
Uniqueness of countable dense linear orders
proven directly for the ordering on the rationals, by constructing a piecewise linear order automorphism with breakpoints at the k {\displaystyle k} given
Cantor's_isomorphism_theorem
PIECEWISE LINEAR
PIECEWISE LINEAR
Surname or Lastname
Scottish
Scottish : nickname for someone with streaks of gray or white hair, from Gaelic riabhach ‘brindled’, ‘grayish’.English : habitational name from either of two places called Reach, in Bedfordshire and Cambridgeshire, from Old English rǣc ‘raised strip of land or other linear feature’ (in the case of the Cambridgeshire name referring to Devil’s Dyke, a post-Roman earthwork).
PIECEWISE LINEAR
PIECEWISE LINEAR
Boy/Male
Arabic, Muslim
Another Name for God; Talented; Apt; Enough
Surname or Lastname
English
English : habitational name from any of various places so called, most of which were originally named with Old English hÄmstede or hÇ£mstede ‘homestead’. One Hempstead in Norfolk derives its name from Old English hænep ‘hemp’ + stede ‘place’, while Hempsted in Gloucestershire was originally ‘high homestead’ (Old English hÄ“ah + hÄmstede).
Girl/Female
Hindu
Happy, Pure, Princess
Girl/Female
Tamil
Shubiksha | à®·à¯à®ªà¯€à®•à¯à®·à®¾
Female
English
Pet form of English Deborah, DEBI means "bee."
Surname or Lastname
German
German : dialect variant of Ammann.English : from a Middle English personal name, Agmund, of Scandinavian origin, from agi ‘awe’ (or possibly agi- ‘point of a sword’) + mund ‘protection’. Compare Hammond.Respelling of French Hamon.
Girl/Female
British, English
The Long Field
Boy/Male
Muslim
Patience, Tolerance, Endurance
Boy/Male
Indian, Sanskrit
Bearer of the Crescent Moon
Male
Native American
Native American Miwok name HOWI means "turtle-dove."
PIECEWISE LINEAR
PIECEWISE LINEAR
PIECEWISE LINEAR
PIECEWISE LINEAR
PIECEWISE LINEAR
a.
Very narrow, and tapering gradually to a fine point from a broadish base; awl-shaped; linear.
n.
A linear apothecium furrowed along the middle; the fruit of certain lichens.
n.
A measure of length, equal to 39.37 English inches, the standard of linear measure in the metric system of weights and measures. It was intended to be, and is very nearly, the ten millionth part of the distance from the equator to the north pole, as ascertained by actual measurement of an arc of a meridian. See Metric system, under Metric.
a.
Shaped like spatula, or like a battledoor, being roundish, with a long, narrow, linear base.
n.
A straight line in space with which a definite linear magnitude termed the pitch is associated (cf. 5th Pitch, 10 (b)). It is used to express the displacement of a rigid body, which may always be made to consist of a rotation about an axis combined with a translation parallel to that axis.
n.
A European perennial herb (Asperula cynanchica) with narrowly linear whorled leaves; -- formerly thought to cure the quinsy. Also called quincewort.
a.
Linear.
a.
Of a linear shape.
n.
An instrument formed by combining prisms so as to correct the chromatic aberration of the light while linear dimensions of objects seen through the prisms are increased or diminished; -- called also prism telescope.
a.
Having the form of a sword, but very long and narrow.
n.
Relative dimensions, without difference in proportion of parts; size or degree of the parts or components in any complex thing, compared with other like things; especially, the relative proportion of the linear dimensions of the parts of a drawing, map, model, etc., to the dimensions of the corresponding parts of the object that is represented; as, a map on a scale of an inch to a mile.
v. t.
To determine the form, extent, position, etc., of, as a tract of land, a coast, harbor, or the like, by means of linear and angular measurments, and the application of the principles of geometry and trigonometry; as, to survey land or a coast.
n.
A painted tape, marked with linear dimensions, as inches, feet, etc., and often inclosed in a case, -- used for measuring.
adv.
In a linear manner; with lines.
a.
Shaped like a tongue; specifically (Bot.), linear or oblong, and fleshy, blunt at the end, and convex beneath; as, a tongue-shaped leaf.
superl.
Not long; having brief length or linear extension; as, a short distance; a short piece of timber; a short flight.
n.
A line, or long, narrow division of anything of a different color or structure from the ground; hence, any linear variation of color or structure; as, a stripe, or streak, of red on a green ground; a raised stripe.
a.
Of or pertaining to a line; consisting of lines; in a straight direction; lineal.
a.
Like a line; narrow; of the same breadth throughout, except at the extremities; as, a linear leaf.
n.
An American endogenous plant (Tradescantia Virginica), with long linear leaves and ephemeral blue flowers. The name is sometimes extended to other species of the same genus.