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Topics referred to by the same term
Interpolation theorem may refer to: Craig interpolation in logic Marcinkiewicz interpolation theorem about non-linear operators Riesz–Thorin interpolation
Interpolation_theorem
Mathematical theory by discovered by Józef Marcinkiewicz
mathematics, particularly in functional analysis, the Marcinkiewicz interpolation theorem, discovered by Józef Marcinkiewicz (1939), is a result bounding
Marcinkiewicz interpolation theorem
Marcinkiewicz_interpolation_theorem
Theorem on operator interpolation
Riesz–Thorin theorem, often referred to as the Riesz–Thorin interpolation theorem or the Riesz–Thorin convexity theorem, is a result about interpolation of operators
Riesz–Thorin_theorem
Theorem in mathematical logic
logic, Craig's interpolation theorem is a result about the relationship between different logical theories. Roughly stated, the theorem says that if a
Craig_interpolation
Sufficiency theorem for reconstructing signals from samples
Whittaker–Nyquist–Shannon, and may also be referred to as the cardinal theorem of interpolation. Sampling is a process of converting a signal (for example, a function
Nyquist–Shannon sampling theorem
Nyquist–Shannon_sampling_theorem
Theorem in mathematical analysis
interpolation theorem, introduced by Sarason (1967), is a generalization of the Caratheodory interpolation theorem and Nevanlinna–Pick interpolation.
Sarason_interpolation_theorem
Form of interpolation
In numerical analysis, polynomial interpolation is the interpolation of a given data set by the polynomial of lowest possible degree that passes through
Polynomial_interpolation
Method for estimating new data within known data points
as "interpolation of operators". The classical results about interpolation of operators are the Riesz–Thorin theorem and the Marcinkiewicz theorem. There
Interpolation
Method of curve fitting
In mathematics, linear interpolation (sometimes lerp) is a method of curve fitting using linear polynomials to construct new data points within the range
Linear_interpolation
Vector space in mathematics
theory of interpolation of vector spaces began by an observation of Józef Marcinkiewicz, later generalized and now known as the Riesz-Thorin theorem. In simple
Interpolation_space
Problem in complex analysis
Nevanlinna–Pick theorem became an area of active research in operator theory following the work of Donald Sarason on the Sarason interpolation theorem. Sarason
Nevanlinna–Pick_interpolation
Operator theorem
lifting theorem, due to Sz.-Nagy and Foias, is a powerful theorem used to prove several interpolation results. The commutant lifting theorem states that
Commutant_lifting_theorem
About simultaneous modular congruences
_{i=1}^{k}B_{i}(X)Q_{i}(X).} A special case of Chinese remainder theorem for polynomials is Lagrange interpolation. For this, consider k monic polynomials of degree
Chinese_remainder_theorem
Conservativity theorem (mathematical logic) Craig's theorem (mathematical logic) Craig's interpolation theorem (mathematical logic) Cut-elimination theorem (proof
List_of_theorems
Formula in matrix theory
Sylvester's formula or Sylvester's matrix theorem (named after J. J. Sylvester) or Lagrange−Sylvester interpolation expresses an analytic function f (A) of
Sylvester's_formula
Polish mathematician (1910–1940)
after Marcinkiewicz include the Marcinkiewicz multiplier theorem, Marcinkiewicz interpolation theorem, and Marcinkiewicz–Zygmund inequality. Following the
Józef_Marcinkiewicz
Signal (re-)construction algorithm
Nyquist–Shannon sampling theorem by Claude Shannon in 1949. It is also commonly called Shannon's interpolation formula and Whittaker's interpolation formula. E. T
Whittaker–Shannon interpolation formula
Whittaker–Shannon_interpolation_formula
polynomial time. This result is not related to the well-known Craig interpolation theorem, although both results are named after the same logician, William
Craig's_theorem
American philosopher (1918–2016)
and the philosophy of science, and he is best known for the Craig interpolation theorem. William Craig was born in Nuremberg, Weimar Republic, on November
William_Craig_(philosopher)
Polynomial interpolation using derivative values
polynomial must satisfy. For another method, see Chinese remainder theorem § Hermite interpolation. For yet another method, see, which uses contour integration
Hermite_interpolation
Mathematical theorem in the study of analysis
directly evaluate polynomials, this theorem has both practical and theoretical relevance, especially in polynomial interpolation. The original version of this
Stone–Weierstrass_theorem
Algebraic expansion of powers of a binomial
binomial theorem, valid for any real exponent, in 1664-5, inspired by the work of John Wallis's Arithmetic Infinitorum and his method of interpolation. A logarithmic
Binomial_theorem
Inequality in mathematical analysis
In the field of mathematical analysis, an interpolation inequality is an inequality of the form ‖ u 0 ‖ 0 ≤ C ‖ u 1 ‖ 1 α 1 ‖ u 2 ‖ 2 α 2 … ‖ u n ‖ n
Interpolation_inequality
Polynomials used for interpolation
scheme. Neville's algorithm Newton form of the interpolation polynomial Bernstein polynomial Carlson's theorem Lebesgue constant The Chebfun system Table
Lagrange_polynomial
Mathematical operator in real and harmonic analysis
strong-type estimate is an immediate consequence of the Marcinkiewicz interpolation theorem: Theorem (Strong Type Estimate). For d ≥ 1, 1 < p ≤ ∞, and f ∈ Lp(Rd)
Hardy–Littlewood maximal function
Hardy–Littlewood_maximal_function
Cryptographic algorithm created by Adi Shamir
formulated the scheme in 1979. The scheme exploits the Lagrange interpolation theorem, specifically that k {\displaystyle k} points on the polynomial
Shamir's_secret_sharing
Method in approximation theory
Mairhuber–Curtis theorem since the basis functions depend on the points of interpolation. Choosing a radial kernel such that the interpolation matrix is non-singular
Radial basis function interpolation
Radial_basis_function_interpolation
Hungarian mathematician
the Riesz extension theorem (which predated the closely related Hahn–Banach theorem). Later, he devised an interpolation theorem to show that the Hilbert
Marcel_Riesz
Theorem in mathematical analysis
of different weak derivatives of a function through an interpolation inequality. The theorem is of particular importance in the framework of elliptic
Gagliardo–Nirenberg interpolation inequality
Gagliardo–Nirenberg_interpolation_inequality
Failure of convergence in interpolation
that occurs when using polynomial interpolation with polynomials of high degree over a set of equispaced interpolation points. It was discovered by Carl
Runge's_phenomenon
many known lists of exceptions. In which case, the classic polynomial interpolation that is located in several variables can be generalized to points that
Alexander–Hirschowitz_theorem
function points, one obtains the simple mean value theorem. Let P {\displaystyle P} be the Lagrange interpolation polynomial for f at x0, ..., xn. Then it follows
Mean value theorem (divided differences)
Mean_value_theorem_(divided_differences)
Function spaces generalizing finite-dimensional p norm spaces
space – Concept within complex analysis Riesz–Thorin theorem – Theorem on operator interpolation Hölder mean – N-th root of the arithmetic mean of the
Lp_space
Mathematical concept
Riesz–Thorin interpolation theorem. The proofs of pointwise convergence for Hilbert and Riesz transforms rely on the Lebesgue differentiation theorem, which
Singular integral operators of convolution type
Singular_integral_operators_of_convolution_type
Theorems connecting continuity to closure of graphs
usually proved using the Riesz–Thorin interpolation theorem and is highly nontrivial. The closed graph theorem can be used to prove a soft version of
Closed graph theorem (functional analysis)
Closed_graph_theorem_(functional_analysis)
Theorem in mathematics
properties of differentiable functions. A special case of this theorem for inverse interpolation of the sine was first described by Parameshvara (1380–1460)
Mean_value_theorem
Branch of mathematical logic
without the cut rule. Gentzen's midsequent theorem, the Craig interpolation theorem, and Herbrand's theorem follow as corollaries of the cut-elimination
Proof_theory
American mathematician
He is known for Lyndon words, the Curtis–Hedlund–Lyndon theorem, Craig–Lyndon interpolation and the Lyndon–Hochschild–Serre spectral sequence. Lyndon
Roger_Lyndon
Theorem in mathematical logic
compactness theorem states that a set of first-order sentences has a model if and only if every finite subset of it has a model. This theorem is an important
Compactness_theorem
Theorem in formal logic
Cut elimination is one of the most powerful tools for proving interpolation theorems. The possibility of carrying out proof search based on resolution
Cut-elimination_theorem
Type of operator in Fourier analysis
multiplier theorem. The proofs of these two theorems are fairly tricky, involving techniques from Calderón–Zygmund theory and the Marcinkiewicz interpolation theorem:
Multiplier_(Fourier_analysis)
Theorem in real analysis
Voorhoeve index. Mean value theorem Intermediate value theorem Linear interpolation Gauss–Lucas theorem "Rolle's theorem | Definition, Equation, & Facts
Rolle's_theorem
Topics referred to by the same term
Joseph Louis Lagrange: Lagrange interpolation formula Lagrange–Bürmann formula Triple product expansion Mean value theorem Euler–Lagrange equation This disambiguation
Lagrange's_formula
Mathematical problem in classical harmonic analysis
another proof, due to Salomon Bochner relies upon the Riesz–Thorin interpolation theorem. For p = 1 and infinity, the result is not true. The construction
Convergence_of_Fourier_series
Polish mathematician (1910–1943)
hyperplane separation theorem are also known (in German) as Trennungssatz von Eidelheit (Eidelheit separation theorem). A theorem on the solubility of
Meier_Eidelheit
Surname list
titles containing Sarason Sarason interpolation theorem, is a generalization of the Caratheodory interpolation theorem and Nevanlinna–Pick Sarasohn This
Sarason
Generalizations of Nyquist-Shannon sampling theorem for reconstructing signals
sampling theorem. Nonuniform sampling is based on Lagrange interpolation and the relationship between itself and the (uniform) sampling theorem. Nonuniform
Nonuniform_sampling
Square matrices satisfy their characteristic equation
In linear algebra, the Cayley–Hamilton theorem (named after the mathematicians Arthur Cayley and William Rowan Hamilton) states that every square matrix
Cayley–Hamilton_theorem
Topics referred to by the same term
Lagrange's four-square theorem, a theorem from number theory Lagrange polynomial for theorems relating to numerical interpolation Euler–Lagrange equation
Lagrange's identity (disambiguation)
Lagrange's_identity_(disambiguation)
Specifies when restoration of a signal by the sampling theorem can become ill-posed
variance noise is added to the samples." In the sampling theorem, the uncertainty of the interpolation as measured by noise variance is the same as the uncertainty
Cheung–Marks_theorem
Lebesgue constant Hermite interpolation Birkhoff interpolation Abel–Goncharov interpolation Spline interpolation — interpolation by piecewise polynomials
List of numerical analysis topics
List_of_numerical_analysis_topics
everywhere in the unit ball. Newman showed that the corona theorem can be reduced to an interpolation problem, which was then proved by Carleson. In 1979 Thomas
Corona_theorem
Algorithms for zeros of functions
in the neighborhood of the root. Many root-finding processes work by interpolation. This consists in using the last computed approximate values of the
Root-finding_algorithm
Changing the resolution of a digital image
include New Edge-Directed Interpolation (NEDI), Edge-Guided Image Interpolation (EGGI), Iterative Curvature-Based Interpolation (ICBI), and Directional
Image_scaling
Theorem in topology
Jordan curve theorem, and the 6-neighbor grid is a precise interpolation between them. The theorem states the following: suppose you put bombs on some squares
Jordan_curve_theorem
Theorem in p-adic analysis
In mathematics, Mahler's theorem, introduced by Kurt Mahler (1958), expresses any continuous p-adic function as an infinite series of certain special
Mahler's_theorem
Theorem
f} at the interpolation points, and does so to the same degree. Let us define the equioscillation condition as the condition in the theorem statement
Equioscillation_theorem
Theorem relating stationary processes' autocorrelations and power spectra
Wiener–Khinchin theorem or Wiener–Khintchine theorem, also known as the Wiener–Khinchin–Einstein theorem or the Khinchin–Kolmogorov theorem, states that
Wiener–Khinchin_theorem
Polish mathematician (1903–1990)
include the Orlicz property, Orlicz category theorem, Mazur-Orlicz theorem, Orlicz interpolation theorem, Musielak-Orlicz space, Orlicz norm, Hardy-Orlicz
Władysław_Orlicz
Theorem in complex analysis
} The three-line theorem also holds for functions with values in a Banach space and plays an important role in complex interpolation theory. It can be
Hadamard_three-lines_theorem
Category in mathematical category theory
Makkai, Michael (1 July 1995). "On Gabbay's Proof of the Craig Interpolation Theorem for Intuitionistic Predicate Logic". Notre Dame Journal of Formal
Coherent_category
Statement in complex analysis
univalent. The Koebe 1/4 theorem provides a related estimate in the case that f {\displaystyle f} is univalent. Nevanlinna–Pick interpolation Kobayashi hyperbolicity
Schwarz_lemma
German mathematician and logician (1932–2024)
S2CID 122569882. Arnold Oberschelp (June 1968). "On the Craig-Lyndon Interpolation Theorem". The Journal of Symbolic Logic. 33 (2): 271–274. doi:10.2307/2269873
Arnold_Oberschelp
allowing for distinctions not permissible in classical logic. interpolation theorem A result stating that if a formula A → B {\displaystyle A\rightarrow
Glossary_of_logic
Construction in transcendental number theory
auxiliary functions, in the 1990s Michel Laurent introduced the idea of interpolation determinants. These are alternants – determinants of matrices of the
Auxiliary_function
Austrian mathematician and holocaust victim (1859–1942)
July 1942. He died there two weeks later. Nevanlinna–Pick interpolation Pick matrix Pick's theorem "Georg Pick - Biography". Georg Alexander Pick at the Mathematics
Georg_Alexander_Pick
American mathematician
New York. Henkin, L. (1963). An Extension of the Craig-Lyndon Interpolation theorem. The Journal of Symbolic Logic. 28(3), 201-216. Henkin, L. (1963)
Leon_Henkin
Root-finding algorithm
means of successive linear interpolation", in Dejon, B.; Henrici, P. (eds.), Constructive Aspects of the Fundamental Theorem of Algebra, London: Wiley-Interscience
Brent's_method
South African philosopher
the former head of the Department of Philosophy. The Craig-Lyndon Interpolation Theorem in 3-Valued Logic, The Journal of Symbolic Logic, Vol. 35, No. 2
R._R._Rockingham_Gill
Argentine mathematician
singular integral operators to partial differential equations, from interpolation theory to Cauchy integrals on Lipschitz curves, from ergodic theory
Alberto_Calderón
form Lagrange form of the remainder Lagrange interpolation Lagrange invariant Lagrange inversion theorem Lagrange multiplier Augmented Lagrangian method
List of things named after Joseph-Louis Lagrange
List_of_things_named_after_Joseph-Louis_Lagrange
Theorem in category theory
In category theory, a branch of mathematics, Beck's monadicity theorem gives a criterion that characterises monadic functors, introduced by Jonathan Mock
Beck's_monadicity_theorem
Sum of the inverses of the positive integers cubed is irrational
In mathematics, Apéry's theorem is a result in number theory which states that Apéry's constant ζ(3) is irrational. That is, the number ζ ( 3 ) = ∑ n
Apéry's_theorem
Function in discrete mathematics
\mathbf {X} } and Y {\displaystyle \mathbf {Y} } . The trigonometric interpolation polynomial p ( t ) = { 1 N [ X 0 + X 1 e i 2 π t + ⋯ + X N 2 − 1 e i
Discrete_Fourier_transform
Extension of classical first-order logic
first-order logic including a compactness theorem, a Löwenheim–Skolem theorem, and a Craig interpolation theorem. (Väänänen, 2007, p. 86). However, Väänänen
Independence-friendly_logic
Signal processing method
Maximal Ripple algorithm imposed an alternating error condition via interpolation and then solved a set of equations that the alternating solution had
Parks–McClellan filter design algorithm
Parks–McClellan_filter_design_algorithm
Birkhoff interpolation: an extension of polynomial interpolation Cubic interpolation Hermite interpolation Lagrange interpolation: interpolation using Lagrange
List_of_algorithms
Characterizes spherical triangles with fixed base and area
In spherical geometry, Lexell's theorem holds that every spherical triangle with the same surface area on a fixed base has its apex on a small circle
Lexell's_theorem
In mathematics, Birkhoff interpolation is an extension of polynomial interpolation. It refers to the problem of finding a polynomial P ( x ) {\displaystyle
Birkhoff_interpolation
Mathematical expression
an interpolation polynomial for a given set of data points. The Newton polynomial is sometimes called Newton's divided differences interpolation polynomial
Newton_polynomial
theorem provides conditions on the lattice under which perfect reconstruction is possible. As with the Nyquist–Shannon sampling theorem, this theorem
Multidimensional_sampling
Family of interpolation and clamping functions
Smoothstep is a family of sigmoid-like interpolation and clamping functions commonly used in computer graphics, video game engines, and machine learning
Smoothstep
Field in logic and theoretical computer science
2307/2275250. JSTOR 2275250. S2CID 44670202. Krajíček, Jan (1997). "Interpolation theorems, lower bounds for proof systems, and independence results for bounded
Proof_complexity
Concept in mathematics
polynomials are widely used, for example in trigonometric interpolation applied to the interpolation of periodic functions. They are used also in the discrete
Trigonometric_polynomial
Movement with a fixed point is rotation
In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the body remains
Euler's_rotation_theorem
Surname list
George D. Birkhoff (crater) Birkhoff interpolation Birkhoff's axioms Birkhoff's theorem (disambiguation), multiple theorems Birkhoff decomposition, two different
Birkhoff
Russian-American mathematician
spaces, Russian Mathematical Surveys, vol. 19, 1964, pp. 65–127 An interpolation theorem for modular spaces, Matematicheskii Sbornik, vol. 108, 1965, pp
Boris_Mityagin
Study of objects of arithmetic interest over infinite towers of number fields
converse to Herbrand's theorem (the so-called Herbrand–Ribet theorem). Karl Rubin found a more elementary proof of the Mazur-Wiles theorem by using Kolyvagin's
Iwasawa_theory
Concept in machine learning
in classical machine learning. The increase usually occurs near the interpolation threshold, where the number of parameters is the same as the number
Double_descent
Theorem in algebraic number theory relating p-adic L-functions and ideal class groups
proved for all primes by Barry Mazur and Andrew Wiles. The Herbrand–Ribet theorem and the Gras conjecture are both easy consequences of the main conjecture
Main conjecture of Iwasawa theory
Main_conjecture_of_Iwasawa_theory
In mathematics, mimetic interpolation is a method for interpolating differential forms. In contrast to other interpolation methods, which estimate a field
Mimetic_interpolation
Topic in mathematics
typical set used in theories of data compression. Roughly speaking, the theorem states that although there are many series of results that may be produced
Asymptotic equipartition property
Asymptotic_equipartition_property
Perpendicular line segment from a triangle's side to opposite vertex
{\displaystyle h_{c}={\sqrt {pq}}} (geometric mean theorem; see special cases, inverse Pythagorean theorem) For acute triangles, the feet of the altitudes
Altitude_(triangle)
Indian mathematician and astronomer (598–668)
Brahmagupta devised and used a special case of the Newton–Stirling interpolation formula of the second-order to interpolate new values of the sine function
Brahmagupta
mathematician. Abel's binomial theorem Abel elliptic functions Abel equation Abel equation of the first kind Abel–Goncharov interpolation Abel–Plana formula Abel
List of things named after Niels Henrik Abel
List_of_things_named_after_Niels_Henrik_Abel
Power series with rational exponents
(non-truncated) Puiseux series and proved the theorem that is now known as Puiseux's theorem or Newton–Puiseux theorem. The theorem asserts that, given an algebraic
Puiseux_series
Field of algebraic geometry
sheaf or line bundle associated to D. This means that, by the Riemann–Roch theorem, the H0 cohomology or space of holomorphic sections is larger than expected
Brill–Noether_theory
Physics theorem of interacting particles
In physics, the poppy-seed bagel theorem concerns interacting particles (e.g., electrons) confined to a bounded surface (or body) A {\displaystyle A}
Poppy-seed_bagel_theorem
iteration, IRKA does an Hermite type interpolation of the original system transfer function. Each interpolation requires solving r {\displaystyle r} shifted
Iterative rational Krylov algorithm
Iterative_rational_Krylov_algorithm
second-order interpolation for computing the positions of the sun and the moon. 665 - Brahmagupta discovers a second order Newton-Stirling interpolation for sin
Timeline of calculus and mathematical analysis
Timeline_of_calculus_and_mathematical_analysis
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