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Topics referred to by the same term
the Schur algorithm may be: The Schur algorithm for expanding a function in the Schur class as a continued fraction The Lehmer–Schur algorithm for finding
Schur_algorithm
Root-finding algorithm
In mathematics, the Lehmer–Schur algorithm (named after Derrick Henry Lehmer and Issai Schur) is a root-finding algorithm for complex polynomials, extending
Lehmer–Schur_algorithm
nth-order polynomial. It is closely related to the Levinson algorithm though Schur algorithm is numerically more stable and better suited to parallel processing
Schur_class
Algorithm in numerical linear algebra
and S. Nash introduced an improved version of the algorithm, known as the Hessenberg–Schur algorithm. It remains a standard approach for solving Sylvester
Bartels–Stewart_algorithm
Schur. Frobenius–Schur indicator Herz–Schur multiplier Jordan–Schur theorem Lehmer–Schur algorithm Schur algebra Schur class Schur's conjecture Schur
List of things named after Issai Schur
List_of_things_named_after_Issai_Schur
Matrix factorisation in mathematics
In linear algebra, the Schur decomposition or Schur triangulation, named after Issai Schur, is a matrix decomposition. It allows one to write an arbitrary
Schur_decomposition
Russian and German mathematician (1875–1941)
Schur's inequality Schur's theorem Schur-convex function Schur–Weyl duality Lehmer–Schur algorithm Schur's property for normed spaces. Jordan–Schur theorem
Issai_Schur
Iterative method for approximating eigenvectors
open source software package ARPACK. Another approach is the Krylov-Schur Algorithm by G. W. Stewart, which is more stable and simpler to implement than
Arnoldi_iteration
Algorithm for finding a zero of a function
be at most ε {\displaystyle \varepsilon } . Binary search algorithm Lehmer–Schur algorithm, generalization of the bisection method in the complex plane
Bisection_method
become viable. The Lehmer–Schur algorithm uses the Schur–Cohn test for circles; a variant, Wilf's global bisection algorithm uses a winding number computation
Polynomial_root-finding
Tool in linear algebra and matrix analysis
The Schur complement is a key tool in the fields of linear algebra, the theory of matrices, numerical analysis, and statistics. It is defined for a block
Schur_complement
Root-finding algorithm for polynomials
Lehmer–Schur algorithm – similar method which uses circles instead of rectangles Herbert S. Wilf (July 1978), "A Global Bisection Algorithm for Computing
Wilf's global bisection algorithm
Wilf's_global_bisection_algorithm
Type of symmetric polynomials in mathematics
In mathematics, Schur polynomials, named after Issai Schur, are certain symmetric polynomials in n variables, indexed by partitions, that generalize the
Schur_polynomial
Root-finding algorithm — algorithms for solving the equation f(x) = 0 General methods: Bisection method — simple and robust; linear convergence Lehmer–Schur algorithm
List of numerical analysis topics
List_of_numerical_analysis_topics
Matrix with shifting rows
the case. Toeplitz systems can be solved by algorithms such as the Schur algorithm or the Levinson algorithm in O ( n 2 ) {\displaystyle O(n^{2})} time
Toeplitz_matrix
Elementwise product of two matrices
Hadamard product (also known as the element-wise product, entrywise product or Schur product) is a binary operation that takes in two matrices of the same dimensions
Hadamard_product_(matrices)
American mathematician (1905–1991)
significant contributions to number theory algorithms for multiprecision integers, such as factoring, Euclid's algorithm, long division, and proof of primality
D._H._Lehmer
Computer program for the Boolean satisfiability problem
As a result, only algorithms with exponential worst-case complexity are known. In spite of this, efficient and scalable algorithms for SAT were developed
SAT_solver
Theorem in linear algebra
matrix. The result is named after Issai Schur (Schur 1911, p. 14, Theorem VII) (note that Schur signed as J. Schur in Journal für die reine und angewandte
Schur_product_theorem
Characteristic polynomial whose associated linear system is stable
Schur stable for discrete-time). In practice, stability is tested via several stability criteria. The Routh–Hurwitz theorem provides an algorithm for
Stable_polynomial
Surname list
director, writer, actor and artist Derrick Lehmer (disambiguation) Lehmer–Schur algorithm, in mathematics, named after Derrick Henry Lehmer Lehmer code Lehmer's
Lehmer
1st episode of the 3rd series of Black Mirror
series of the British science fiction anthology series Black Mirror. Michael Schur and Rashida Jones wrote the teleplay for the episode, based on a story by
Nosedive_(Black_Mirror)
Mathematical formula for the number of Young tableaux
number of semi-standard Young tableaux, which is a specialization of a Schur polynomial. Let λ = ( λ 1 ≥ ⋯ ≥ λ k ) {\displaystyle \lambda =(\lambda _{1}\geq
Hook_length_formula
Algorithm to calculate eigenvalues
In numerical linear algebra, the QR algorithm or QR iteration is an eigenvalue algorithm: that is, a procedure to calculate the eigenvalues and eigenvectors
QR_algorithm
Polynomial root-finding algorithm
Aitken's delta-squared process Graeffe's method Horner's method Lehmer-Schur algorithm List of things named after members of the Bernoulli family Polynomial
Bernoulli's_method
Matrix B such that B² equals a given matrix A
1990 Deadman, Edvin; Higham, Nicholas J.; Ralha, Rui (2013), "Blocked Schur Algorithms for Computing the Matrix Square Root" (PDF), Applied Parallel and Scientific
Square_root_of_a_matrix
desired destination via an alternate available path. According to Shuster & Schur (1974, p. 1): The heuristic approach to problem solving consists of applying
Heuristic_routing
Concept in mathematics
correspondence, also referred to as the RSK correspondence or RSK algorithm, is a combinatorial bijection between matrices A with non-negative integer
Robinson–Schensted–Knuth correspondence
Robinson–Schensted–Knuth_correspondence
"Multidimensional Nonlinear Schur Parametrization of NonGaussian Stochastic Signals, Part Two: Generalized Schur Algorithm". Multidimensional Systems and
Non-linear multi-dimensional signal processing
Non-linear_multi-dimensional_signal_processing
Topics referred to by the same term
containing Shor Schor, Schore, Schoor/van Schoor, Schorr, Shor, Shore, Shorr, Schur This disambiguation page lists articles associated with the title Shor.
Shor
polynomials Rogers polynomials Rogers–Szegő polynomials Rook polynomial Schur polynomials Shapiro polynomials Sheffer sequence Spread polynomials Tricomi–Carlitz
List_of_polynomial_topics
Mathematical rule
coefficients that arise when decomposing a product of two Schur functions as a linear combination of other Schur functions. These coefficients are natural numbers
Littlewood–Richardson_rule
Subfield of convex optimization
cc}t&c^{T}x\\c^{T}x&d^{T}x\end{array}}\right]} We can use the theory of Schur Complements to see that D ⪰ 0 {\displaystyle D\succeq 0} (Boyd and Vandenberghe
Semidefinite_programming
Recursive algorighm in linear algebra
Trench and S. Zohar, respectively. Other methods to process data include Schur decomposition and Cholesky decomposition. In comparison to these, Levinson
Levinson_recursion
Machine learning framework for portfolio construction
mean-variance optimization (MVO) framework developed by Harry Markowitz. HRP algorithms apply discrete mathematics and machine learning techniques to create diversified
Hierarchical_Risk_Parity
including the refutation of the Schur-Klin conjecture on Schur rings over a cyclic group, a polynomial-time algorithm for recognizing and testing isomorphism
Sergei_Evdokimov
value decomposition Higher-order singular value decomposition Schur decomposition Schur complement Haynsworth inertia additivity formula Matrix equivalence
Outline_of_linear_algebra
Equation from stability analysis
the discrete case, the Schur method of Kitagawa is often used. For the continuous Lyapunov equation the Bartels–Stewart algorithm can be used. Defining
Lyapunov_equation
n\geq 0} , are briefly called finite p-groups. The p-group generation algorithm by M. F. Newman and E. A. O'Brien is a recursive process for constructing
P-group_generation_algorithm
Representation theory Schur's lemma Coset enumeration Schreier's subgroup lemma Schreier–Sims algorithm Todd–Coxeter algorithm Computer algebra system
List_of_group_theory_topics
{\displaystyle x_{2}} during the iteration for the Schur complement system and thus obtain an efficient algorithm. We start the conjugate gradient iteration by
Uzawa_iteration
Representation of a matrix as a product
the complex Schur form which has the eigenvalues of A along its diagonal. Comment: if A is a normal matrix, then T is diagonal and the Schur decomposition
Matrix_decomposition
Iterative method in conformal mapping
Dirichlet problem must be solved jointly on the two subdomains. An iterative algorithm is introduced: Make a first guess of the solution on the circle's boundary
Schwarz_alternating_method
American mathematician
Introduction: Issai Schur and the Early Development of the Schur Complement", The Schur Complement and Its Applications, Numerical Methods and Algorithms, vol. 4
Emilie_Virginia_Haynsworth
Dutch computer scientist
mathematical conjectures such as the Boolean Pythagorean triples problem, Schur's theorem number 5, and Keller's conjecture in dimension seven. Heule received
Marijn_Heule
Polynomial that permutes a ring
102. Fried, M. (1970). "On a conjecture of Schur". Michigan Math. J.: 41–55. Turnwald, G. (1995). "On Schur's conjecture". J. Austral. Math. Soc. 58 (3):
Permutation_polynomial
Undirected graph acted on by a vertex-transitive cyclic group of symmetries
Pöschel, Reinhard (2001), "The isomorphism problem for circulant graphs via Schur ring theory", Codes and association schemes (Piscataway, NJ, 1999), DIMACS
Circulant_graph
c s {\displaystyle a'_{kl}=a_{kl}(c^{2}-s^{2})+(a_{kk}-a_{ll})cs} . The Schur decomposition determines the rotation angle angle, θ, or more conveniently
Jacobi_rotation
Mathematical proof at least partially generated by computer
hdl:2445/192693. S2CID 28258285. Heule, Marijn J. H. (2017). "Schur Number Five". arXiv:1711.08076 [cs.LO]. "Schur Number Five". www.cs.utexas.edu. Retrieved 2021-10-06
Computer-assisted_proof
Mathematical test in control system theory
handled by the Schur–Cohn criterion, the Jury test and the Bistritz test. The Routh test can be derived through the use of the Euclidean algorithm and Sturm's
Routh–Hurwitz stability criterion
Routh–Hurwitz_stability_criterion
Software library for numerical linear algebra
implement the associated matrix factorizations such as LU, QR, Cholesky and Schur decomposition. The routines handle both real and complex matrices in both
LAPACK
Integer that is a perfect square modulo some integer
{q}}\log \log q\right).} This result cannot be substantially improved, for Schur had proved in 1918 that max N | ∑ n = 1 N ( n q ) | > 1 2 π q {\displaystyle
Quadratic_residue
Method of determining if a discrete linear time-invariant system is stable
than previously available stability tests for discrete systems like the Schur–Cohn and the Jury test. In the following, the focus is only on how to test
Bistritz_stability_criterion
Topics referred to by the same term
Complement (group theory) Complementary subspaces Orthogonal complement Schur complement Complement (complexity), relating to decision problems and complexity
Complement
Matrix defined using smaller matrices called blocks
and C are conformable with them for partitioning. Furthermore, A and the Schur complement of A in P: P/A = D − CA−1B must be invertible. Equivalently,
Block_matrix
German mathematician (1912–1991)
ISBN 978-0-521-59669-5. Cantor, David G.; Zassenhaus, Hans (April 1981), "A new algorithm for factoring polynomials over finite fields", Mathematics of Computation
Hans_Zassenhaus
Mathematical problem
an algorithm for computing the Frobenius number in polynomial time (in the logarithms of the coin denominations forming an input). No known algorithm is
Coin_problem
Matrix equation in control theory
{\displaystyle B} into Schur form by a QR algorithm, and then solving the resulting triangular system via back-substitution. This algorithm, whose computational
Sylvester_equation
Native American showrunner, screenwriter, filmmaker, and weaver
NBC (Peacock) comedy series Rutherford Falls, alongside Ed Helms and Mike Schur. Known for writing and production work on shows such as Brooklyn Nine-Nine
Sierra_Teller_Ornelas
Vector satisfying some of the criteria of an eigenvector
value decomposition Higher-order singular value decomposition Schur decomposition Schur complement Haynsworth inertia additivity formula Reducing subspace
Generalized_eigenvector
the one-dimensional, s = 0 case, answering a question of Issai Schur. An algorithmic version of the Fekete problem is number 7 on the list of problems
Fekete_problem
Matrix decomposition
of the Q matrices from the steps in the algorithm. (For more general matrices, the QR algorithm yields the Schur decomposition first, from which the eigenvectors
Eigendecomposition of a matrix
Eigendecomposition_of_a_matrix
Polynomial whose roots are the eigenvalues of a matrix
form has stronger properties, but these are sufficient; alternatively the Schur decomposition can be used, which is less popular but somewhat easier to
Characteristic_polynomial
Optimization problem
Networks. 11 (2): 109–124. doi:10.1002/net.3230110205. Shuster, Kenneth A.; Schur, Dennis A. (1974). Heuristic Routing for Solid Waste Collection Vehicles
Vehicle_routing_problem
of things named after Bernhard Riemann List of things named after Issai Schur List of things named after Anatoliy Skorokhod List of things named after
Lists_of_mathematics_topics
Mathematical function generalizing the determinant and permanent
group. Littlewood and Richardson studied the relation of the immanant to Schur functions in the representation theory of the symmetric group. The necessary
Immanant
Type of group in abstract algebra
theory of the symmetric group plays a fundamental role through the ideas of Schur functors. In the theory of Coxeter groups, the symmetric group is the Coxeter
Symmetric_group
Number-theoretical function
of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions, and Schur Functions. Springer Science & Business Media. p. 9. ISBN 1402004915. Grosswald
Sum_of_squares_function
Mathematical group
Coset Optimal solutions for Rubik's Cube Solvable group Thistlethwaite's algorithm Not to be confused with E {\displaystyle E} as used in the extended Singmaster
Rubik's_Cube_group
platforms, etc. EPS provides iterative algorithms for linear eigenvalue problems. Krylov methods such as Krylov-Schur, Arnoldi and Lanczos. Davidson methods
SLEPc
Mathematical identities related to integer partitions
they then published a joint new proof (Rogers & Ramanujan 1919). Issai Schur (1917) independently rediscovered and proved the identities. The Rogers–Ramanujan
Rogers–Ramanujan_identities
Function in discrete mathematics
the DFT is usually computed by efficient fast Fourier transform (FFT) algorithms. The DFT is used in many practical applications of Fourier analysis. In
Discrete_Fourier_transform
Algebraic curve in mathematics
EdDSA digital signature algorithm Elliptic-curve Diffie–Hellman key exchange (ECDH) Elliptic curve digital signature algorithm (ECDSA) Supersingular isogeny
Elliptic_curve
In mathematics, invariant of square matrices
proven using either the Leibniz formula or a factorization involving the Schur complement, is det ( A 0 C D ) = det ( A ) det ( D ) = det ( A B 0 D )
Determinant
Theorems that help decompose a finite group based on prime factors of its order
in H itself. The algorithmic version of this (and many improvements) is described in textbook form in Butler, including the algorithm described in Cannon
Sylow_theorems
discriminant together with the form itself (of degree 1 and order 2). (Schur 1968, II.8) (Hilbert 1993, XVI, XX) The algebra of invariants of the cubic
Invariant_of_a_binary_form
Nonlinear equation which arises on linear optimal control problems
the eigenvalues of Z that are inside the unit circle. Lyapunov equation Schur decomposition Sylvester equation Chow, Gregory (1975). Analysis and Control
Algebraic_Riccati_equation
Branch of mathematics that studies the properties of groups
parts, in turn, are much more easily manageable than the whole V (via Schur's lemma). Given a group G, representation theory then asks what representations
Group_theory
Immediate opinionated/controversial statement on news events
History of Bad Sports Writing". Pacific Standard. Retrieved 13 April 2015. Schur, Mike (April 13, 2018). "Do You Get the Show". Slate. Retrieved 2019-02-11
Hot_take
German mathematician (1849–1917)
Charles W. (2003), Pioneers of Representation Theory: Frobenius, Burnside, Schur, and Brauer, History of Mathematics, Providence, R.I.: American Mathematical
Ferdinand_Georg_Frobenius
Specification of a mathematical group by generators and relations
presentations of G. The deficiency of a finite group is non-positive. The Schur multiplicator of a finite group G can be generated by −def(G) generators
Presentation_of_a_group
Array of numbers
matrices. To avoid numerically ill-conditioned situations, further algorithms such as the Schur decomposition can be employed. Matrices can be generalized in
Matrix_(mathematics)
Algebraic structure
the symmetric group and the partition algebra generalizes the original Schur-Weyl duality between the general linear group and the symmetric group. There
Partition_algebra
the associated matrix factorizations (LU, Cholesky, QR, SVD, Schur, and generalized Schur). MATLAB is a widely used proprietary software to perform numerical
List of numerical-analysis software
List_of_numerical-analysis_software
_{21}(t)} . Since the Schur complement is positive definite for the real t {\displaystyle t} away from the poles and the Schur complement is a rational
Polynomial matrix spectral factorization
Polynomial_matrix_spectral_factorization
unknowns in the interiors of the subdomain, thus reducing the problem to the Schur complement on the subdomain interface. Since the BDD preconditioner involves
Balancing domain decomposition method
Balancing_domain_decomposition_method
Special kind of square matrix
they are very important in numerical analysis. By the LU decomposition algorithm, an invertible matrix may be written as the product of a lower triangular
Triangular_matrix
Mathematical transform that expresses a function of time as a function of frequency
class (meaning conjugation-invariant) functions that map from G to C by Schur's lemma. The group T is no longer finite but still compact, and it preserves
Fourier_transform
property testing. Notable algorithms include the Babai's algorithm for finding random group elements, the Product Replacement Algorithm, and testing group commutativity
Black_box_group
American comedy musician (born 1959)
Yankovic as an influence on his musical Hamilton. Television producer Michael Schur considered that Yankovic's music represented a "deep egalitarian spirit
"Weird_Al"_Yankovic
unchanged under permutations of the weight. In turn this implies that the Schur function of a partition is a symmetric function. Bender–Knuth involutions
Bender–Knuth_involution
Counting polynomial real roots based on coefficients
together listing all the roots. This approach is used in the fastest algorithms today for computer computation of real roots of polynomials (see real-root
Descartes'_rule_of_signs
Mathematical concept
theorems Hall's theorem p-group Elementary abelian group Frobenius group Schur multiplier Classification of finite simple groups cyclic alternating Lie
Hyperbolic_group
History of a branch of mathematics
with Sophus Lie, followed by work of Wilhelm Killing, Eduard Study, Issai Schur, Ludwig Maurer, and Élie Cartan. The discontinuous (discrete group) theory
History_of_group_theory
Matrix equal to its conjugate-transpose
targets Normal matrix – Matrix that commutes with its conjugate transpose Schur–Horn theorem – Characterizes the diagonal of a Hermitian matrix with given
Hermitian_matrix
Theorem about projections of coadjoint orbits of a connected compact Lie group
derive Lie-theoretical extensions of the Golden–Thompson inequality and the Schur–Horn theorem for Hermitian matrices. Konstant's convexity theorem states
Kostant's_convexity_theorem
German mathematician (1804–1851)
to introduce and study the symmetric polynomials that are now known as Schur polynomials, giving the so-called bialternant formula for these, which is
Carl_Gustav_Jacob_Jacobi
Math operation methods
/\mathbf {A} :=\mathbf {D} -\mathbf {C} \mathbf {A} ^{-1}\mathbf {B} } is the Schur complement of A. (A must be square, so that it can be inverted. Furthermore
Methods_of_matrix_inversion
1 B ) = {\displaystyle (D-CA^{-1}B)=} a much smaller matrix called the Schur complement of A {\displaystyle A} . This is the FKF method that may make
Fast_Kalman_filter
a numerical method to verify unistochasticity based on the algorithm by Haagerup The Schur-Horn theorem is equivalent to the following "weak convexity"
Unistochastic_matrix
travel, tourism, insurance
SCHUR ALGORITHM
SCHUR ALGORITHM
Boy/Male
Tamil
Wall, Ox, That beholds
Surname or Lastname
English
English : nickname for a beautiful or radiant person, or one with fair hair, from Middle English scher, schir ‘bright’, ‘fair’.
Surname or Lastname
English
English : from Middle English shoe ‘shoe’ (Old English scÅh), applied as a metonymic occupational name for a shoemaker or possibly a topographic name for someone who lived on a shoe-shaped piece of land.Translation of Schuh.
Boy/Male
Hindu
Wall, Ox, That beholds
Surname or Lastname
English
English : variant of Shear 1.Jewish (eastern Ashkenazic) : variant spelling of Scher.
Surname or Lastname
English
English : topographic name for someone who lived among rushes or occupational name for someone who made things out of rushes (see Rush).Americanized spelling of German Rüscher (variant of Rusch) or Roscher.
Surname or Lastname
English
English : variant of Rusher.Americanized spelling of German Rischer, a nickname for a hasty or impetuous person, from an agent derivative of Middle High German rischen ‘to rush’.Americanized spelling of Swiss German Rüscher, a topographic name for someone who lived on a mountainside, from southern dialect risch ‘slope’, ‘mountainside’ + -er, suffix denoting an inhabitant.Americanized spelling of North German Rischer, a topographic name from Middle Low German risch ‘reed’, a topographic name for someone who lived where reeds grew.Anglicized form of Eastern German Rischar, a nickname from Sorbian rýsar ‘knight’.
Surname or Lastname
English
English : regional name from the southern English county so called, which derives its name from Hampton (i.e. the port of Southampton) + Old English scīr ‘division’, ‘district’.English : regional name from the area of Hallamshire in southern Yorkshire, named from Hallam + Middle English schir ‘division’, ‘administrative region’ (Old English scīr). The surname is most common in Yorkshire, where this second derivation is most likely to be the source.
Surname or Lastname
English
English : unexplained.Probably also an Americanized spelling of German and Jewish Schuh.
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 (Sussex)
English (Sussex) : unexplained.Americanized form of German Löscher (see Loescher).Jewish (eastern Ashkenazic) : habitational name for someone from the village of Lasha, now in Belarus.
Surname or Lastname
English, Scottish, and Irish
English, Scottish, and Irish : variant of Usher 1, with the Old French definite article prefixed.Translation of French Lussier, L’Huissier with the French definite article retained. Compare Lafontaine.Americanized spelling of German Lüscher (see Luscher).
Boy/Male
British, English
Peasant
Surname or Lastname
English
English : topographic name from Middle English score ‘steep place’ (Old English scoru), or a habitational name from Score in Ilfracombe or Scur Farm in Braunton, Devon.
Boy/Male
Anglo Saxon
Storm.
Surname or Lastname
English (mainly Yorkshire)
English (mainly Yorkshire) : occupational name for an archer, Middle English schut(te), schit(te) (from Old English scytta, a primary derivative of scēotan ‘to shoot’).Americanized spelling of German Schutt.
Surname or Lastname
English
English : variant of Brach 2, the suffix -er denoting an inhabitant.Probably a partly Americanized form of Swiss German Bretscher, an occupational name for a sawyer, from Brett ‘plank’, ‘board’ + scher, a reduced form of Scherer ‘cutter’, a derivative of scheren ‘to cut’, ‘sever’.
Biblical
wall; ox; that beholds
SCHUR ALGORITHM
SCHUR ALGORITHM
SCHUR ALGORITHM
SCHUR ALGORITHM
SCHUR ALGORITHM
SCHUR ALGORITHM
SCHUR ALGORITHM
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