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Topics referred to by the same term
Minimum polynomial can refer to: Minimal polynomial (field theory) Minimal polynomial (linear algebra) This disambiguation page lists articles associated
Minimum_polynomial
Failure of convergence in interpolation
oscillation at the edges of an interval that occurs when using polynomial interpolation with polynomials of high degree over a set of equispaced interpolation
Runge's_phenomenon
Polynomial function of degree 4
local maximum and another local minimum. The degree four (quartic case) is the highest degree such that every polynomial equation can be solved by radicals
Quartic_function
In mathematics, minimum polynomial extrapolation is a sequence transformation used for convergence acceleration of vector sequences, due to Cabay and Jackson
Minimum polynomial extrapolation
Minimum_polynomial_extrapolation
Estimate of time taken for running an algorithm
Quasi-polynomial time algorithms are algorithms whose running time exhibits quasi-polynomial growth, a type of behavior that may be slower than polynomial time
Time_complexity
Method for estimating new data outside known data points
Wikimedia Commons has media related to Extrapolation. Forecasting Minimum polynomial extrapolation Multigrid method Overfitting Prediction interval Regression
Extrapolation
Pair of polynomial sequences
The Chebyshev polynomials are two sequences of orthogonal polynomials related to the cosine and sine functions, notated as T n ( x ) {\displaystyle T_{n}(x)}
Chebyshev_polynomials
Statistics concept
In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable
Polynomial_regression
Topics referred to by the same term
specification to provide more expressive qualities for performing music Minimum polynomial extrapolation, a sequence transformation algorithm used for convergence
MPE
Mathematical optimization problem
method. Cut canceling: a general dual method. Minimum mean cycle canceling: a simple strongly polynomial algorithm. Successive shortest path and capacity
Minimum-cost_flow_problem
Polynomial function of degree two
function, is a quadratic polynomial, a polynomial of degree two. In elementary mathematics a polynomial and its associated polynomial function are rarely distinguished
Quadratic_function
Computational complexity class
of a polynomial-time approximation scheme whose running time is quasi-polynomial rather than polynomial. Problems with a QPTAS include minimum-weight
Quasi-polynomial_time
Partition of a graph by removing fewest possible edges
be solved in polynomial time by the Stoer-Wagner algorithm. A generalization of the minimum cut problem without terminals is the minimum k-cut, in which
Minimum_cut
On short connecting nets with added points
to the minimum spanning tree. However, while both the non-negative shortest path and the minimum spanning tree problem are solvable in polynomial time,
Steiner_tree_problem
Every polynomial has a real or complex root
non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since
Fundamental theorem of algebra
Fundamental_theorem_of_algebra
Complexity class
have a solution space just as large, but can be solved in polynomial time (for example minimum spanning tree). On the other hand, there are NP-problems
NP-completeness
Least-weight tree connecting graph vertices
Esau-Williams and Sharma produce solutions close to optimal in polynomial time. The degree-constrained minimum spanning tree is a MST in which each vertex is connected
Minimum_spanning_tree
Arithmetic in a field with a finite number of elements
ISBN 978-0-387-21846-5 Gordon, G. (1976). "Very simple method to find the minimum polynomial of an arbitrary nonzero element of a finite field". Electronics Letters
Finite_field_arithmetic
Type of approximation algorithm
In computer science (particularly algorithmics), a polynomial-time approximation scheme (PTAS) is a type of approximation algorithm for optimization problems
Polynomial-time approximation scheme
Polynomial-time_approximation_scheme
Set of edges without common vertices
{\displaystyle ~2.37\leq \omega <3} . However, no polynomial-time algorithm is known for finding a minimum maximal matching, that is, a maximal matching that
Matching_(graph_theory)
Type of linear code
In coding theory, a polynomial code is a type of linear code whose set of valid code words consists of those polynomials (usually of some fixed length)
Polynomial_code
Computational problem in graph theory
finding the maximum-weight or minimum-weight closure in a vertex-weighted directed graph. It may be solved in polynomial time using a reduction to the
Maximum_flow_problem
Geometry of the location of polynomial roots
In mathematics, a univariate polynomial of degree n with real or complex coefficients has n complex roots (if counted with their multiplicities). They
Geometrical properties of polynomial roots
Geometrical_properties_of_polynomial_roots
Cryptographic algorithm created by Adi Shamir
specifically that k {\displaystyle k} points on the polynomial uniquely determines a polynomial of degree less than or equal to k − 1 {\displaystyle
Shamir's_secret_sharing
Error-correcting codes
take the inverse transform (polynomial interpolation) of C(x) to produce c(x). The Singleton bound states that the minimum distance d of a linear block
Reed–Solomon_error_correction
Mathematical function defined piecewise by polynomials
function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields
Spline_(mathematics)
Subset of a graph's vertices, including at least one endpoint of every edge
problem of finding a minimum vertex cover is a classical optimization problem. It is NP-hard, so it cannot be solved by a polynomial-time algorithm if P
Vertex_cover
Model selection principle
Minimum Description Length (MDL) is a model selection principle where the shortest description of the data is the best model. MDL methods learn through
Minimum_description_length
Complexity class
every problem L which can be solved in non-deterministic polynomial-time, there is a polynomial-time reduction from L to H. That is, assuming a solution
NP-hardness
Polynomial sequence
In mathematics, the Bernoulli polynomials, named after Jacob Bernoulli, combine the Bernoulli numbers and binomial coefficients. They are used for series
Bernoulli_polynomials
Study of numbers that are not solutions of polynomials with rational coefficients
non-constant polynomial with rational coefficients (or equivalently, by clearing denominators, with integer coefficients) then that polynomial will have
Transcendental_number_theory
Automorphism group of the Klein quartic
the order of an element in the class, the size of the class, the minimum polynomial of every representative in GL(3, 2), and the function notation for
PSL(2,7)
Polynomial equation of degree 6
In algebra, a sextic (or hexic) polynomial is a polynomial of degree six. A sextic equation is a polynomial equation of degree six—that is, an equation
Sextic_equation
Error correction code
GF(24) based on the reducing polynomial z4 + z + 1, using primitive element α(z) = z. There are fourteen minimum polynomials mi(x) with coefficients in
BCH_code
Subset of a graph's edges
problem that belongs to the class of covering problems and can be solved in polynomial time. Formally, an edge cover of a graph G is a set of edges C such that
Edge_cover
Linear optimal control technique
theory of optimal control is concerned with operating a dynamic system at minimum cost. The case where the system dynamics are described by a set of linear
Linear–quadratic_regulator
Artificial river barrier
A polynomial weir is a weir that has a geometry defined by a polynomial equation of any order n. In practice, most weirs are low-order polynomial weirs
Weir
Relating coefficients and roots of a polynomial
In mathematics, Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots. They are named after François Viète (1540-1603)
Vieta's_formulas
Mathematical construct in computer algebra
Gröbner basis is a particular kind of generating set of an ideal in a polynomial ring K [ x 1 , … , x n ] {\displaystyle K[x_{1},\ldots ,x_{n}]} over a
Gröbner_basis
List of unsolved computational problems
factorization be done in polynomial time on a classical (non-quantum) computer? Can the discrete logarithm be computed in polynomial time on a classical (non-quantum)
List of unsolved problems in computer science
List_of_unsolved_problems_in_computer_science
Algorithm to smooth data points
fitting successive sub-sets of adjacent data points with a low-degree polynomial by the method of linear least squares. When the data points are equally
Savitzky–Golay_filter
Mathematical operator acting on sequences
integer sequences. Aitken's delta-squared process Anderson acceleration Minimum polynomial extrapolation Richardson extrapolation Series acceleration Steffensen's
Sequence_transformation
Hungarian and American mathematician and physicist (1903–1957)
Neumann's first published paper was On the position of zeroes of certain minimum polynomials, co-authored with Michael Fekete and published when von Neumann was
John_von_Neumann
delta-squared process — most useful for linearly converging sequences Minimum polynomial extrapolation — for vector sequences Richardson extrapolation Shanks
List of numerical analysis topics
List_of_numerical_analysis_topics
Edges that hit all cycles in a graph
in exponential time, or in fixed-parameter tractable time. In polynomial time, the minimum feedback arc set can be approximated to within a polylogarithmic
Feedback_arc_set
Mathematical technique for improving convergence
eliminates the largest part of the absolute error. Shanks transformation Minimum polynomial extrapolation Van Wijngaarden transformation Abramowitz, Milton; Stegun
Series_acceleration
Polynomial function of degree 5
and a is nonzero. In other words, a quintic function is defined by a polynomial of degree five. Because they have an odd degree, normal quintic functions
Quintic_function
Roots of multiple multivariate polynomials
of polynomial equations (sometimes simply a polynomial system) is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials in
System of polynomial equations
System_of_polynomial_equations
Method for estimating new data within known data points
this interpolant with a polynomial of higher degree. Consider again the problem given above. The following sixth degree polynomial goes through all the seven
Interpolation
Tree which includes all vertices of a graph
Xuong tree and an associated maximum-genus embedding can be found in polynomial time. A tree is a connected undirected graph with no cycles. It is a spanning
Spanning_tree
Method for solving quadratic equations
algebra, completing the square is a technique for converting a quadratic polynomial of the form a x 2 + b x + c {\displaystyle \textstyle ax^{2}+bx+c}
Completing_the_square
Classification of algorithm
discovery that showed there is a factoring algorithm with a huge but provably polynomial time bound, that would change our beliefs about factoring. The algorithm
Galactic_algorithm
Point set triangulation minimizing total length
exactly in polynomial time. The minimum weight triangulation has also sometimes been called the optimal triangulation. The problem of minimum weight triangulation
Minimum-weight_triangulation
Quadratic polynomial
complex quadratic polynomial is a quadratic polynomial whose coefficients and variable are complex numbers. Quadratic polynomials have the following
Complex_quadratic_polynomial
Graph theory concept
graphs, finding the minimum degree spanning tree is also NP-hard. R. Krishman and B. Raghavachari (2001) have a quasi-polynomial time approximation algorithm
Minimum_degree_spanning_tree
Combinatorial optimization problem
assignment in time polynomial in n. The assignment problem is a special case of the transportation problem, which is a special case of the minimum cost flow problem
Assignment_problem
Theory of getting acceptably close inexact mathematical calculations
arithmetic. This is accomplished by using a polynomial of high degree, and/or narrowing the domain over which the polynomial has to approximate the function. Narrowing
Approximation_theory
Skeletonized version of algebraic geometry
In mathematics, tropical geometry is the study of polynomials and their geometric properties when addition is replaced with minimization and multiplication
Tropical_geometry
Minimum-cost tree with exactly k vertices
be solved in polynomial time by a brute-force search algorithm that tries all k-tuples of vertices. However, for variable k, the k-minimum spanning tree
K-minimum_spanning_tree
Polynomials in combinatorial mathematics
In combinatorial mathematics, the Bell polynomials, named in honor of Eric Temple Bell, are used in the study of set partitions. They are related to Stirling
Bell_polynomials
Counting polynomial real roots based on coefficients
described by René Descartes in his La Géométrie, counts the roots of a polynomial by examining sign changes in its coefficients. The number of positive
Descartes'_rule_of_signs
Mathematical method for approximating solutions to differential and integral equations
to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called
Collocation_method
Problem in graph theory
finding a minimum cut is known to be efficiently solvable via the Ford–Fulkerson algorithm. As the maximum cut problem is NP-hard, no polynomial-time algorithms
Maximum_cut
Mathematical modelling alogorithm
GMDH iteratively generates and evaluates candidate models, often using polynomial functions, and selects the best-performing ones based on an external criterion
Group_method_of_data_handling
Cycles in a graph that generate all cycles
edges of the graph have positive weights, the minimum weight cycle basis may be constructed in polynomial time. In planar graphs, the set of bounded cycles
Cycle_basis
In mathematics, a form (i.e. a homogeneous polynomial) h(x) of degree 2m in the real n-dimensional vector x is sum of squares of forms (SOS) if and only
Polynomial_SOS
Point where the derivative of a function is zero or undefined (in certain cases)
discriminant of f viewed as a polynomial in y with coefficients that are polynomials in x. This discriminant is thus a polynomial in x which has the critical
Critical_point_(mathematics)
Polynomial function of degree 3
b x 2 + c x + d , {\displaystyle f(x)=ax^{3}+bx^{2}+cx+d,} that is, a polynomial function of degree three. In many texts, the coefficients a, b, c, and
Cubic_function
Type of signal processing filter
operator. The denominator is a Butterworth polynomial in s {\displaystyle s} . The Butterworth polynomials may be written in complex form as above, but
Butterworth_filter
Class of computational problems
all minimum cuts between different pairs of terminal vertices. Algorithms for constructing flows include Dinic's algorithm, a strongly polynomial algorithm
Network_flow_problem
Automatic mechanical calculator
difference engine is an automatic mechanical calculator designed to tabulate polynomial functions. It was designed in the 1820s, and was created by Charles Babbage
Difference_engine
Methodic assignment of colors to elements of a graph
Birkhoff introduced the chromatic polynomial to study the coloring problem, which was generalised to the Tutte polynomial by W. T. Tutte, both of which are
Graph_coloring
Subset of a graph's nodes such that all other nodes link to at least one
approximation ratio: for any α, a polynomial-time α-approximation algorithm for minimum dominating sets would provide a polynomial-time α-approximation algorithm
Dominating_set
Type of hash function
input as a polynomial, but over the Galois field GF(2). Instead of seeing the input as a polynomial of bytes, it is seen as a polynomial of bits, and
Rolling_hash
Type of analog or digital filter
because its mathematical characteristics are derived from Chebyshev polynomials. Type I Chebyshev filters are usually referred to as "Chebyshev filters"
Chebyshev_filter
Partition of a graph's nodes into 2 disjoint subsets
sum of the cut-edge weights of any minimum cut that separates the source and the sink are equal. There are polynomial-time methods to solve the min-cut
Cut_(graph_theory)
Algebraic study of differential equations
solutions, similarly as polynomial algebras are used for the study of algebraic varieties, which are solution sets of systems of polynomial equations. Weyl algebras
Differential_algebra
Product of a number by itself
polynomials, other expressions, or values in systems of mathematical values other than the numbers. For instance, the square of the linear polynomial
Square_(algebra)
Branch of mathematics
graphs, and especially the chromatic polynomial, the Tutte polynomial and knot invariants. The chromatic polynomial of a graph, for example, counts the
Algebraic_graph_theory
In control theory, when an LTI system and its inverse are causal and stable
theory and signal processing, a linear, time-invariant system is said to be minimum-phase if the system and its inverse are causal and stable. The most general
Minimum_phase
Subfield of mathematical optimization
(e.g. reservoir flow-rates) There is a large amount of literature on polynomial-time algorithms for certain special classes of discrete optimization.
Combinatorial_optimization
Subfield of mathematical optimization
over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard
Convex_optimization
Unrelated vertices in graphs
approximated to within any approximation ratio c < 1 in polynomial time; similar polynomial-time approximation schemes exist in any family of graphs
Independent set (graph theory)
Independent_set_(graph_theory)
Combinatorial optimization problem
k-center problem can not be (optimally) solved in polynomial time. However, there are some polynomial time approximation algorithms that get near-optimal
Metric_k-center
Method to solve optimization problems
polynomial-time algorithm? Does LP admit a strongly polynomial-time algorithm to find a strictly complementary solution? Does LP admit a polynomial-time
Linear_programming
Partition of a graph's nodes into cliques
number in perfect graphs in polynomial time. Another class of graphs in which the minimum clique cover can be found in polynomial time are the triangle-free
Clique_cover
A fully polynomial-time approximation scheme (FPTAS) is an algorithm for finding approximate solutions to function problems, especially optimization problems
Fully polynomial-time approximation scheme
Fully_polynomial-time_approximation_scheme
Generalization of network flow problems
commodities, one for each pair of nodes. Éva Tardos (1985). "A strongly polynomial minimum cost circulation algorithm". Combinatorica. 5 (3): 247–255. doi:10
Circulation_problem
tree, or Minimum spanning tree for a subset of the vertices of a graph. (The minimum spanning tree for an entire graph is solvable in polynomial time.)
List_of_NP-complete_problems
Statistical approach
obtain an optimal response. Box and Wilson suggest using a second-degree polynomial model to do this. They acknowledge that this model is only an approximation
Response_surface_methodology
target spatial frequency). From the experimental MRTD data, a general polynomial best fit is calculated and the result is the MRTD curve which gives direct
Minimum resolvable temperature difference
Minimum_resolvable_temperature_difference
Min-ULR[≥] is polynomial in some special case. Min-ULR[=,>,≥] can be approximated within n + 1 in polynomial time. Min-ULR[>,≥] are minimum-dominating-set-hard
Minimum relevant variables in linear system
Minimum_relevant_variables_in_linear_system
Error-correcting codes used in wireless communication
the variables of the polynomial, and the values c S ∈ { 0 , 1 } {\textstyle c_{S}\in \{0,1\}} are the coefficients of the polynomial. Note that there are
Reed–Muller_code
up extrapolation in Wiktionary, the free dictionary. Forecasting Minimum polynomial extrapolation Multigrid method Prediction interval Regression analysis
Interior_reconstruction
Subexponential bound in computational complexity
science, a function f ( n ) {\displaystyle f(n)} is said to exhibit quasi-polynomial growth when it has an upper bound of the form f ( n ) = 2 O ( ( log
Quasi-polynomial_growth
Methods for locating real roots of a polynomial
isolation of a polynomial consist of producing disjoint intervals of the real line, which contain each one (and only one) real root of the polynomial, and, together
Real-root_isolation
Finding shortest walks through all graph edges
edges with the minimum possible total weight) so that the resulting multigraph does have an Eulerian circuit. It can be solved in polynomial time, unlike
Chinese_postman_problem
Polynomial equation of degree two
non-negative integers, and therefore it is a polynomial equation. In particular, it is a second-degree polynomial equation, since the greatest power is two
Quadratic_equation
Choosing the fewest coins to make a given amount of money
the coins. It is weakly NP-hard, but may be solved optimally in pseudo-polynomial time by dynamic programming. Coin values can be modeled by a set of n
Change-making_problem
Independent set which is not a subset of any other independent set
researchers have studied algorithms that list all maximal independent sets in polynomial time per output set. The time per maximal independent set is proportional
Maximal_independent_set
MINIMUM POLYNOMIAL
MINIMUM POLYNOMIAL
Boy/Male
Bengali, Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Sanskrit
Plenty; Maximum; Intelligent; Young and Dynamic; Earth
Girl/Female
Christian, Gujarati, Hindu, Indian, Kannada, Marathi, Sindhi, Telugu
Wished-for Child
Boy/Male
Irish
Is the Irish form of Old English ead “â€richâ€â€ + mund “â€guardianâ€â€, and implies “â€guardian of the riches.â€â€ In more recent times the name has been given to honor Eamon De Valera who was President of Ireland for 14 years, the maximum allowed, from 1959 to 1973.
Girl/Female
Tamil
Wished for child
Boy/Male
Irish
Is the Irish form of Old English ead “â€richâ€â€ + mund “â€guardianâ€â€, and implies “â€guardian of the riches.â€â€ In more recent times the name has been given to honor Eamon De Valera who was President of Ireland for 14 years, the maximum allowed, from 1959 to 1973.
Girl/Female
Arabic, Muslim
Increase; Excess; High Degree; Maximum; Feminine of Mazid
Boy/Male
Irish
Is the Irish form of Old English ead “â€richâ€â€ + mund “â€guardianâ€â€, and implies “â€guardian of the riches.â€â€ In more recent times the name has been given to honor Eamon De Valera who was President of Ireland for 14 years, the maximum allowed, from 1959 to 1973.
Boy/Male
African, Arabic
Far
Girl/Female
English, Hindu, Indian, Marathi
Small Daughter
MINIMUM POLYNOMIAL
MINIMUM POLYNOMIAL
Boy/Male
Hindu, Indian
King of Saints
Girl/Female
Hindu, Indian, Malayalam
Ray
Girl/Female
Hindu
City
Girl/Female
Hindu, Indian, Marathi
Possessing Beauty
Female
English
(Greek ΟφÎλια): Feminine form of Greek Ophelos, OPHELIA means "help." This name was used by Shakespeare for an ill-omened character in Hamlet.
Girl/Female
English
At the elder tree.
Female
English
From an English byname derived from a pet form of the word maid, MAIDIE means "young woman."Â
Boy/Male
Arthurian Legend
Prince killed by Tristan.
Girl/Female
Afghan, American, Arabic, Australian, British, Chinese, Christian, Danish, Dutch, English, French, German, Hindu, Indian, Irish, Italian, Latin, Netherlands
Slang Term for Woman; Blind One
Boy/Male
Tamil
Lord muraga (Son of Shivan)
MINIMUM POLYNOMIAL
MINIMUM POLYNOMIAL
MINIMUM POLYNOMIAL
MINIMUM POLYNOMIAL
MINIMUM POLYNOMIAL
a.
Greatest in quantity or highest in degree attainable or attained; as, a maximum consumption of fuel; maximum pressure; maximum heat.
pl.
of Minimum
n.
Minimum.
n.
A small American bird (Empidonax minimus); the least flycatcher.
a.
Of the color of red or vermilion.
n.
Anything very minute; as, the minims of existence; -- applied to animalcula; and the like.
n.
The greatest quantity or value attainable in a given case; or, the greatest value attained by a quantity which first increases and then begins to decrease; the highest point or degree; -- opposed to minimum.
n.
The little finger; the fifth digit, or that corresponding to it, in either the manus or pes.
n.
A heavy, brilliant red pigment, consisting of an oxide of lead, Pb3O4, obtained by exposing lead or massicot to a gentle and continued heat in the air. It is used as a cement, as a paint, and in the manufacture of flint glass. Called also red lead.
n.
A being of the smallest size.
pl.
of Minimus
n.
A self-registering thermometer, especially one that registers the maximum and minimum during long periods.
v. t.
To reduce to the smallest part or proportion possible; to reduce to a minimum.
n.
A minim.
n.
In a curve referred to polar coordinates, any point for which the radius vector is a maximum or minimum.
a.
Of the color of minium or red lead; miniate.
pl.
of Maximum
n.
The least quantity assignable, admissible, or possible, in a given case; hence, a thing of small consequence; -- opposed to maximum.
n.
A kind of minium, or red lead, made by calcining carbonate of lead, but inferior to true minium.
n.
A coarse umbelliferous plant of Europe (Tordylium maximum).