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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 , a ≠ 0 , {\displaystyle f(x)=ax^{2}+bx+c
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
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
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)
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
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
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
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
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
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
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
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
Association of one output to each input
definition of the function.) Functions can be classified by the nature of formulas that define them: A quadratic function is a function that may be written
Function_(mathematics)
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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 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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
rational function . Pythagorean theorem . Pythagorean trigonometric identity . quadratic function In algebra, a quadratic function, a quadratic polynomial
Glossary_of_calculus
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
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
Algorithm for finding zeros of functions
and that f is a smooth function. So, even before any computation, it is known that any convergent Newton iteration has a quadratic rate of convergence.
Newton's_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
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
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
Least squares approximation of linear functions to data
Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems
Linear_least_squares
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
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
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
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)
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)
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
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
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
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
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
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
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
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
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
Combinatorial optimization problem
except that the cost function is expressed in terms of quadratic inequalities, hence the name. The formal definition of the quadratic assignment problem
Quadratic_assignment_problem
Principle and applications of MINFLUX microscopy
position r → {\displaystyle {\vec {r}}} can be approximated by a quadratic function. Therefore, the recorded number of emission photons is: n ( r → ,
Minflux
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
Function defined by a hypergeometric series
then there is a quadratic transformation of the hypergeometric function, connecting it to a different value of z related by a quadratic equation. The first
Hypergeometric_function
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
Number assigned to each electron shell in an atom
described below, the total energy of an electron is a negative inverse quadratic function of the principal quantum number n, leading to degenerate energy levels
Principal_quantum_number
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
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
Mathematical formula expressing equality
letters at the beginning, a, b, c, d, ... . For example, the general quadratic equation is usually written ax2 + bx + c = 0. The process of finding the
Equation
Function used in signal processing
processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside
Window_function
Branch of differential geometry
general relativity. On the other hand, replacing the quadratic form by a more general non-quadratic function leads to Finsler geometry. There exists a close
Riemannian_geometry
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
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)
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
Convex optimization problem
the SOCP is equivalent to a convex quadratically constrained linear program. Convex quadratically constrained quadratic programs can also be formulated as
Second-order_cone_programming
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
Approximation method in statistics
uncertainty Orthogonal projection Proximal gradient methods for learning Quadratic loss function Root mean square Squared deviations from the mean Charnes, A.;
Least_squares
QUADRATIC FUNCTION
QUADRATIC FUNCTION
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Male
Egyptian
, a high Egyptian functionary.
Male
Egyptian
, Functionary of the Interior.
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.
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.
Biblical
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Male
Egyptian
, a great functionary.
Male
Egyptian
, an Egyptian functionary.
Male
Egyptian
, the son of the functionary Heknofre.
Male
Celtic
, great justiciary, or functionary.
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.
Male
Egyptian
, an Egyptian functionary.
QUADRATIC FUNCTION
QUADRATIC FUNCTION
Girl/Female
Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Telugu
Content; Goddess of Flower
Boy/Male
Hindu, Indian
Strong Loyal Person
Boy/Male
Tamil
Song
Boy/Male
Indian, Punjabi, Sikh
For whom Soul is the Holy Place
Girl/Female
Indian, Sanskrit
Awakened; Roused; Expanded
Girl/Female
Muslim
One who is loved and respected by all
Male
Spanish
Portuguese and Spanish form of Roman Latin Julius, JULIO means "descended from Jupiter (Jove)."
Boy/Male
Muslim
Another name of God, One who preaches
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi
Lord Indra
Girl/Female
Hindu, Indian, Marathi
A Part
QUADRATIC FUNCTION
QUADRATIC FUNCTION
QUADRATIC FUNCTION
QUADRATIC FUNCTION
QUADRATIC FUNCTION
a.
Pertaining to terms of the second degree; as, a quadratic equation, in which the highest power of the unknown quantity is a square.
a.
Tetragonal.
a.
Of or pertaining to the biquadrate, or fourth power.
p. pr. & vb. n.
of Quadrate
a.
To square; to agree; to suit; to correspond; -- followed by with.
pl.
of Quadratrix
n.
Same as Quadrate.
n.
A quadrat.
a.
A quadrate; a square.
pl.
of Quadratrix
a.
Of or pertaining to the quadrate and jugal bones.
n.
A biquadratic equation.
a.
Of or pertaining to a square, or to squares; resembling a quadrate, or square; square.
n.
That branch of algebra which treats of quadratic equations.
n.
A curve made use of in the quadrature of other curves; as the quadratrix, of Dinostratus, or of Tschirnhausen.
imp. & p. p.
of Quadrate
a.
Quadrate; square.
v. t.
To adjust (a gun) on its carriage; also, to train (a gun) for horizontal firing.
n.
A biquadrate.
a.
The quadrate bone.