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Polynomial function of degree two
In mathematics, a quadratic function of a single variable is a function of the form f ( x ) = a x 2 + b x + c {\displaystyle f(x)=ax^{2}+bx+c} with
Quadratic_function
Polynomial equation of degree two
solutions of the equation, and roots or zeros of the quadratic function on its left-hand side. A quadratic equation has at most two solutions. If there is
Quadratic_equation
Solving an optimization problem with a quadratic objective function
Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks
Quadratic_programming
Formula that provides the solutions to a quadratic equation
algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation. Other ways of solving quadratic equations,
Quadratic_formula
Linear optimal control technique
by a quadratic function is called the LQ problem. One of the main results in the theory is that the solution is provided by the linear–quadratic regulator
Linear–quadratic_regulator
Mathematical relation assigning a probability event to a cost
regression theory, which is based on the quadratic loss function. The quadratic loss function is also used in linear-quadratic optimal control problems. In these
Loss_function
Polynomial function of degree 4
quartic function is a cubic function. Sometimes the term biquadratic is used instead of quartic, but, usually, biquadratic function refers to a quadratic function
Quartic_function
Plane curve: conic section
another plane that is tangential to the conical surface. The graph of a quadratic function y = a x 2 + b x + c {\displaystyle y=ax^{2}+bx+c} (with a ≠ 0 {\displaystyle
Parabola
Independent parameter describing the state of a physical system
is often useful to specify quadratic degrees of freedom. These are degrees of freedom that contribute in a quadratic function to the energy of the system
Degrees of freedom (physics and chemistry)
Degrees_of_freedom_(physics_and_chemistry)
Function whose squared absolute value has finite integral
square-integrable function, also called a quadratically integrable function or L 2 {\displaystyle L^{2}} function or square-summable function, is a real- or
Square-integrable_function
Method for solving quadratic equations
also used for graphing quadratic functions, deriving the quadratic formula, and more generally in computations involving quadratic polynomials, for example
Completing_the_square
Address collision resolution scheme
Quadratic probing is an open addressing scheme in computer programming for resolving hash collisions in hash tables. Quadratic probing operates by taking
Quadratic_probing
Polynomial function of degree 3
solutions are called roots of the function. The derivative of a cubic function is a quadratic function. A cubic function with real coefficients has either
Cubic_function
Real function with secant line between points above the graph itself
number), a quadratic function c x 2 {\displaystyle cx^{2}} ( c {\displaystyle c} as a nonnegative real number) and an exponential function c e x {\displaystyle
Convex_function
Continuous probability distribution
and statistics, the U-quadratic distribution is a continuous probability distribution defined by a unique convex quadratic function with lower limit a and
U-quadratic_distribution
Optimization problem in mathematics
quadratically constrained quadratic program (QCQP) is an optimization problem in which both the objective function and the constraints are quadratic functions
Quadratically constrained quadratic program
Quadratically_constrained_quadratic_program
Association of one output to each input
include constant functions, linear functions and quadratic functions. Rational functions are quotients of two polynomial functions, and their domain
Function_(mathematics)
Topics referred to by the same term
for square. Quadratic function (or quadratic polynomial), a polynomial function that contains terms of at most second degree Complex quadratic polynomials
Quadratic
Circle associated with a quadratic equation
associated with a quadratic equation; it is named after Thomas Carlyle. The circle has the property that the solutions of the quadratic equation are the
Carlyle_circle
Probability distribution
+Y_{m}^{2}\right)/m}}\sim F_{n,m}.} A quadratic form of a normal vector, i.e. a quadratic function q = ∑ x i 2 + ∑ x j + c {\textstyle q=\sum x_{i}^{2}+\sum
Normal_distribution
Equation explaining wages via schooling and experience
logarithm of earnings is modelled as the sum of years of education and a quadratic function of "years of potential experience". ln w = f ( s , x ) = ln w
Mincer_earnings_function
Concept in mathematics
generalizes the conjugate gradient method to nonlinear optimization. For a quadratic function f ( x ) {\displaystyle \displaystyle f(x)} f ( x ) = ‖ A x − b ‖ 2
Nonlinear conjugate gradient method
Nonlinear_conjugate_gradient_method
Function defined by multiple sub-functions
mathematics, a piecewise function (also called a piecewise-defined function, a hybrid function, or a function defined by cases) is a function whose domain is partitioned
Piecewise_function
Mathematical function
chemistry to form basis sets. Gaussian functions arise by composing the exponential function with a concave quadratic function: f ( x ) = exp ( α x 2 + β x
Gaussian_function
Simple polynomial map exhibiting chaotic behavior
The logistic map is a discrete dynamical system defined by the quadratic difference equation It is a recurrence relation and a polynomial mapping of degree 2
Logistic_map
Class of probability distributions
subset of NEF, called NEF with quadratic variance function (NEF-QVF) because the variance can be written as a quadratic function of the mean. NEF-QVF are discussed
Natural_exponential_family
Study of mathematical algorithms for optimization problems
difficult than regular linear programming. Quadratic programming allows the objective function to have quadratic terms, while the feasible set must be specified
Mathematical_optimization
Family of solutions to related differential equations
\alpha t\,dt.\end{aligned}}} Bessel functions can be described as Fourier transforms of powers of quadratic functions. For example (for Re(ω) > 0): 2 K
Bessel_function
straight line. Quadratic function: Second degree polynomial, graph is a parabola. Cubic function: Third degree polynomial. Quartic function: Fourth degree
List of mathematical functions
List_of_mathematical_functions
Collective decision-making procedure
various issues. The number of votes to add is determined by a quadratic cost function, which means that the number of votes a person casts for a given
Quadratic_voting
Size of a two-dimensional surface
planimeter mechanical device. To find the bounded area between two quadratic functions, we first subtract one from the other, writing the difference as
Area
Product of a number by itself
function. The dot product of a Euclidean vector with itself is equal to the square of its length: v⋅v = v2. This is further generalised to quadratic forms
Square_(algebra)
Hash collision resolution technique
set to 1. Quadratic probing in which the interval between probes increases linearly (hence, the indices are described by a quadratic function). Double
Open_addressing
Mathematical optimization algorithm
{\displaystyle \mathbf {x} _{*}} is also the unique minimizer of the following quadratic function f ( x ) = 1 2 x T A x − x T b , x ∈ R n . {\displaystyle f(\mathbf
Conjugate_gradient_method
Concept in the analysis of dynamical systems
constructing Lyapunov functions for ODEs, in many specific cases the construction of Lyapunov functions is known. For instance, quadratic functions suffice for
Lyapunov_function
Mathematical operation
second derivative is related to the best quadratic approximation for a function f. This is the quadratic function whose first and second derivatives are
Second_derivative
Curve from a cone intersecting a plane
A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola
Conic_section
Function with unusual fractal properties
question-mark function, denoted ?(x), is a function with unusual fractal properties, defined by Hermann Minkowski in 1904. It maps quadratic irrational numbers
Minkowski's question-mark function
Minkowski's_question-mark_function
Formulation of classical mechanics using momenta
{q}},{\boldsymbol {\dot {q}}})} T {\displaystyle T} is a homogeneous quadratic function in q ˙ {\displaystyle {\boldsymbol {\dot {q}}}} Regarding extensions
Hamiltonian_mechanics
Function in number theory
the Legendre symbol is a function of a {\displaystyle a} and p {\displaystyle p} defined as ( a p ) = { 1 if a is a quadratic residue modulo p and
Legendre_symbol
Gives conditions for the solvability of quadratic equations modulo prime numbers
theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime
Quadratic_reciprocity
Measure of difference between two points
{\displaystyle t} , then f {\displaystyle f} is a quadratic function. Proof idea: For any quadratic function q : S → R {\displaystyle q:S\to \mathbb {R} }
Bregman_divergence
Polynomial equation of degree 4
discriminant of the quadratic function become zero. To explain this, first expand a perfect square so that it equals a quadratic function: ( s u + t ) 2 =
Quartic_equation
Polynomial with all terms of degree two
In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example, 4 x
Quadratic_form
Variable used for specification
that determine which particular quadratic function is being considered. A parameter could be incorporated into the function name to indicate its dependence
Parameter
Mathematical proportionality to a square
mathematics, a function or sequence is said to exhibit quadratic growth when its values are proportional to the square of the function argument or sequence
Quadratic_growth
Optimization algorithm
a quadratic minimization problem. If the system matrix A {\displaystyle \mathbf {A} } is real symmetric and positive-definite, an objective function is
Gradient_descent
Algorithms for solving convex optimization problems
\\\end{aligned}}} We assume that the constraint functions belong to some family (e.g. quadratic functions), so that the program can be represented by a
Interior-point_method
Conjecture on zeros of the zeta function
discriminant of an imaginary quadratic number field K. Assume the generalized Riemann hypothesis for L-functions of all imaginary quadratic Dirichlet characters
Riemann_hypothesis
Kind of probability distribution
(or generalized chi-square distribution) is the distribution of a quadratic function of a multinormal variable (normal vector), or a linear combination
Generalized chi-squared distribution
Generalized_chi-squared_distribution
Periodic motion of the atoms of a molecule
harmonic motion. In this approximation, the vibrational energy is a quadratic function (parabola) with respect to the atomic displacements and the first
Molecular_vibration
Function equal to the product of its values on coprime factors
known as quadratic functions or specially multiplicative functions. Euler's function φ ( n ) {\displaystyle \varphi (n)} is a totient function, and the
Multiplicative_function
Function or value which does not change
depend on the main variable(s) in question. For example, a general quadratic function is commonly written as a x 2 + b x + c {\displaystyle ax^{2}+bx+c}
Constant_(mathematics)
Property of a mathematical matrix
positive definite if and only if its quadratic form is a strictly convex function. More generally, any quadratic function from R n {\displaystyle \mathbb {R}
Definite_matrix
Combinatorial optimization problem
Quadratic unconstrained binary optimization (QUBO), also known as unconstrained binary quadratic programming (UBQP), is a combinatorial optimization problem
Quadratic unconstrained binary optimization
Quadratic_unconstrained_binary_optimization
Artificial neural network node function
activation functions. Usually the sinusoid is used, as any periodic function is decomposable into sinusoids by the Fourier transform. Quadratic activation
Activation_function
Set of methods for supervised statistical learning
problem is a quadratic function of the c i {\displaystyle c_{i}} subject to linear constraints, it is efficiently solvable by quadratic programming algorithms
Support_vector_machine
Function used in Lagrangian mechanics
is more common. Moreover, the original theory is generalized from quadratic functions q ↦ R ( q ˙ ) = 1 2 q ˙ ⋅ V q ˙ {\displaystyle q\mapsto R({\dot {q}})={\frac
Rayleigh_dissipation_function
Least squares approximation of linear functions to data
distribution distributed random variables. A generalization of the LTF is the Quadratic Template Fit, which assumes a second order regression of the model, requires
Linear_least_squares
Quantum search algorithm
require exponentially many steps, and Grover's algorithm provides at most a quadratic speedup over the classical solution for unstructured search, this suggests
Grover's_algorithm
Statistical method
; Mirkes, E.M.; Zinovyev, A. (2016) "Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning." Neural Networks
Lasso_(statistics)
elsewhere. Linear and convex quadratic functions are self-concordant, since their third derivative is zero. Any function f ( x ) = − log ( − g ( x )
Self-concordant_function
Method for solving continuous operator problems (such as differential equations)
of a quadratic function representing the system energy and the approximate solution is a linear combination of the given set of the basis functions. Bubnov–Galerkin
Galerkin_method
Nearest integers from a number
Floor and ceiling functions In mathematics, the floor function is the function that takes a real number x as input and returns the greatest integer less
Floor_and_ceiling_functions
Method of calculating an investment's rate of return
cash flows; the NPV is a quadratic function of 1/(1 + r), where r is the rate of return, or put differently, a quadratic function of the discount rate r/(1 + r);
Internal_rate_of_return
Loss function used in robust regression
\left(|a|-{\frac {1}{2}}\delta \right),&{\text{otherwise.}}\end{cases}}} This function is quadratic for small values of a, and linear for large values, with equal values
Huber_loss
Method for finding stationary points of a function
x_{k+1}=x_{k}+t} . If the second derivative is positive, the quadratic approximation is a convex function of t {\displaystyle t} , and its minimum can be found
Newton's method in optimization
Newton's_method_in_optimization
the family of quadratic functions having the general form y = a x 2 + b x + c , {\displaystyle y=ax^{2}+bx+c\,,} the simplest function is y = x 2 {\displaystyle
Parent_function
Family of continuous probability distributions
values in the probability mass function of the hypergeometric distribution (which yields the linear-divided-by-quadratic structure). In equation (1), the
Pearson_distribution
Root of a quadratic polynomial with a unit leading coefficient
number theory, quadratic integers are a generalization of the usual integers to quadratic fields. A complex number is called a quadratic integer if it
Quadratic_integer
Combinatorial optimization method for a family of functions of discrete variables
of functions that can be optimised through graph cuts, such as submodular quadratic functions. Graph cut optimization can be extended to functions of
Graph_cut_optimization
Mathematical concept
quadratic irrational number (also known as a quadratic irrational or quadratic surd) is an irrational number that is the solution to some quadratic equation
Quadratic_irrational_number
The quadratic knapsack problem (QKP), first introduced in 19th century, is an extension of knapsack problem that allows for quadratic terms in the objective
Quadratic_knapsack_problem
Type of homogeneous polynomial of degree 2
In mathematics, a definite quadratic form is a quadratic form over some real vector space V that has the same sign (always positive or always negative)
Definite_quadratic_form
Theorem for proving more complex theorems
contexts. Often, a theorem is broken into multiple cases (for example, a quadratic function may have no real roots, one double root, or two distinct roots), and
Lemma_(mathematics)
Quantum algorithm for solving systems of linear equations
Hassidim, and Seth Lloyd. Specifically, the algorithm estimates quadratic functions of the solution vector to a given system. The algorithm is one of
HHL_algorithm
Measure of inequality of a statistical distribution
with a quadratic function across pairs of intervals or building an appropriately smooth approximation to the underlying distribution function that matches
Gini_coefficient
Quadratic homogeneous polynomial in two variables
In mathematics, a binary quadratic form is a quadratic homogeneous polynomial in two variables q ( x , y ) = a x 2 + b x y + c y 2 , {\displaystyle q(x
Binary_quadratic_form
Method for estimating the unknown parameters in a linear regression model
the OLS estimator for β. The function S(b) is quadratic in b with positive-definite Hessian, and therefore this function possesses a unique global minimum
Ordinary_least_squares
Subfield of mathematical optimization
the constraints are all linear, but the objective may be a convex quadratic function. Second order cone programming are more general. Semidefinite programming
Convex_optimization
Operation in mathematical calculus
the function yield better approximations to the integral, can be carried further: Simpson's rule approximates the integrand by a piecewise quadratic function
Integral
Branch of pure mathematics
century. Gauss proved in this work the law of quadratic reciprocity and developed the theory of quadratic forms. He also introduced some basic notation
Number_theory
Algorithms for zeros of functions
last two computed points. Three values define a parabolic curve: a quadratic function. This is the basis of Muller's method. Although all root-finding algorithms
Root-finding_algorithm
Multivalued function in mathematics
a quadratic polynomial in x: where r1 and r2 are real distinct constants, the roots of the quadratic polynomial. Here, the solution is a function which
Lambert_W_function
Field (mathematics) generated by the square root of an integer
theory, a quadratic field is an algebraic number field of degree two over Q {\displaystyle \mathbf {Q} } , the rational numbers. Every such quadratic field
Quadratic_field
Optimization algorithm
Sequential quadratic programming (SQP) is an iterative method for constrained nonlinear optimization, also known as Lagrange-Newton method. SQP methods
Sequential quadratic programming
Sequential_quadratic_programming
scheme – in a 1979 paper. In order to find the cell face value a quadratic function passing through two bracketing or surrounding nodes and one node on
QUICK_scheme
Equation from stability analysis
globally asymptotically stable. The quadratic function V ( x ) = x T P x {\displaystyle V(x)=x^{T}Px} is a Lyapunov function that can be used to verify stability
Lyapunov_equation
Stage of electronic circuit design
placement. Quadratic placement is an early analytical method that models interconnect length by a quadratic function and uses high-performance quadratic optimization
Placement (electronic design automation)
Placement_(electronic_design_automation)
Sum type in number theory
combination of the values of the complex exponential function with coefficients given by a quadratic character; for a general character, one obtains a more
Quadratic_Gauss_sum
In statistics, the rational quadratic covariance function is used in spatial statistics, geostatistics, machine learning, image analysis, and other fields
Rational quadratic covariance function
Rational_quadratic_covariance_function
Special functions of several complex variables
including abelian varieties, moduli spaces, quadratic forms, and solitons. Theta functions in two dimensions are functions of two complex arguments. In one choice
Theta_function
Mechanical property that measures stiffness of a solid material
Young's modulus is a function of the strain, so the second equivalence no longer holds, and the elastic energy is not a quadratic function of the strain: u
Young's_modulus
Statistical method
the second partial derivative test by noting that the variance is a quadratic function of the weights. Thus, the minimum variance of the estimator is then
Inverse-variance_weighting
rational function . Pythagorean theorem . Pythagorean trigonometric identity . quadratic function In algebra, a quadratic function, a quadratic polynomial
Glossary_of_calculus
Concept in mathematical invariant theory
the biquadratic function of x, y was first brought into notice as an invariant by Mr Boole; and the discriminant of the quadratic function of x, y is identical
Catalecticant
Group theory function
bound. The Dehn functions for SL(m,Z), where m > 4 are quadratic. The Dehn function of SL(4,Z), has been conjectured to be quadratic, by Thurston. This
Dehn_function
Quadratic programming as a special case
frequently in computational mechanics and encompasses the well-known quadratic programming as a special case. It was proposed by Cottle and Dantzig in 1968
Linear complementarity problem
Linear_complementarity_problem
Polynomial function: defined by evaluating a polynomial. Linear function; also affine function. Quadratic function Cubic function Quartic function Quintic
List_of_types_of_functions
Flaw in mathematical modelling
this simple function with a new, more complex quadratic function, or with a new, more complex linear function on more than two independent variables, carries
Overfitting
QUADRATIC FUNCTION
QUADRATIC FUNCTION
Surname or Lastname
English (chiefly Kent and Sussex)
English (chiefly Kent and Sussex) : occupational name for a designer or engineer, from a Middle English reduced form of Old French engineor ‘contriver’ (a derivative of engaigne ‘cunning’, ‘ingenuity’, ‘stratagem’, ‘device’). Engineers in the Middle Ages were primarily designers and builders of military machines, although in peacetime they might turn their hands to architecture and other more pacific functions.German : from the Latin personal name Januarius (see January 1). Jänner is a South German word for ‘January’, and so it is possible that this is one of the surnames acquired from words denoting months of the year, for example by converts who had been baptized in that month, people who were born or baptized in that month, or people whose taxes were due in January.
Biblical
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Male
Egyptian
, a great functionary.
Male
Egyptian
, an Egyptian functionary.
Male
Celtic
, great justiciary, or functionary.
Surname or Lastname
English
English : occupational name for a dresser of cloth, Old English fullere (from Latin fullo, with the addition of the English agent suffix). The Middle English successor of this word had also been reinforced by Old French fouleor, foleur, of similar origin. The work of the fuller was to scour and thicken the raw cloth by beating and trampling it in water. This surname is found mostly in southeast England and East Anglia. See also Tucker and Walker.In a few cases the name may be of German origin with the same form and meaning as 1 (from Latin fullare).Americanized version of French Fournier.Samuel Fuller (1589–1633), born in Redenhall, Norfolk, England, was among the Pilgrim Fathers who sailed on the Mayflower in 1620. He was a deacon of the church and until his death functioned as Plymouth Colony’s physician.
Surname or Lastname
English
English : nickname from the animal, Middle English catte ‘cat’. The word is found in similar forms in most European languages from very early times (e.g. Gaelic cath, Slavic kotu). Domestic cats were unknown in Europe in classical times, when weasels fulfilled many of their functions, for example in hunting rodents. They seem to have come from Egypt, where they were regarded as sacred animals.English : from a medieval female personal name, a short form of Catherine.Variant spelling of German and Dutch Katt.
Surname or Lastname
English
English : topographic name for someone who lived by the gates of a medieval walled town. The Middle English singular gate is from the Old English plural, gatu, of geat ‘gate’ (see Yates). Since medieval gates were normally arranged in pairs, fastened in the center, the Old English plural came to function as a singular, and a new Middle English plural ending in -s was formed. In some cases the name may refer specifically to the Sussex place Eastergate (i.e. ‘eastern gate’), known also as Gates in the 13th and 14th centuries, when surnames were being acquired.Americanized spelling of German Götz (see Goetz).Translated form of French Barrière (see Barriere).In New England, Gates was the preferred English version of the name of an extensive French family, called Barrière dit Langevin.
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Male
Egyptian
, the son of the functionary Heknofre.
Male
Egyptian
, an Egyptian functionary.
Male
Egyptian
, a high Egyptian functionary.
Male
Egyptian
, Functionary of the Interior.
QUADRATIC FUNCTION
QUADRATIC FUNCTION
Biblical
the generation of God
Girl/Female
Hindu, Indian
Wonder
Boy/Male
Hindu, Indian, Marathi, Sanskrit
Bestower of Wealth
Boy/Male
Polish
God's glory.
Girl/Female
American, Australian, British, English
Skylark; Lark
Boy/Male
Muslim/Islamic
Joy solved
Boy/Male
Tamil
Mantavyah | மாஂநà¯à®¤à®¾à®µà¯à®¯à®¾à®¹Â
Sadhu
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Tamil, Telugu
Beloved
Boy/Male
Indian
Gain
Girl/Female
Australian, French, Hawaiian, Hebrew
Beautiful; Lovely
QUADRATIC FUNCTION
QUADRATIC FUNCTION
QUADRATIC FUNCTION
QUADRATIC FUNCTION
QUADRATIC FUNCTION
n.
Same as Quadrate.
a.
Tetragonal.
a.
The quadrate bone.
pl.
of Quadratrix
a.
Pertaining to terms of the second degree; as, a quadratic equation, in which the highest power of the unknown quantity is a square.
n.
A curve made use of in the quadrature of other curves; as the quadratrix, of Dinostratus, or of Tschirnhausen.
a.
A quadrate; a square.
p. pr. & vb. n.
of Quadrate
a.
Of or pertaining to a square, or to squares; resembling a quadrate, or square; square.
imp. & p. p.
of Quadrate
a.
Of or pertaining to the quadrate and jugal bones.
pl.
of Quadratrix
a.
To square; to agree; to suit; to correspond; -- followed by with.
n.
That branch of algebra which treats of quadratic equations.
v. t.
To adjust (a gun) on its carriage; also, to train (a gun) for horizontal firing.
n.
A quadrat.
n.
A biquadrate.
a.
Of or pertaining to the biquadrate, or fourth power.
a.
Quadrate; square.
n.
A biquadratic equation.