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Improved reduction for specific matrices
In numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas), is a simplified form
Tridiagonal_matrix_algorithm
Matrix with nonzero elements on the main diagonal and the diagonals above and below it
the Lanczos algorithm. A tridiagonal matrix is a matrix that is both upper and lower Hessenberg matrix. In particular, a tridiagonal matrix is a direct
Tridiagonal_matrix
Algorithm to calculate eigenvalues
convergence of the QR algorithm. If the original matrix is symmetric, then the upper Hessenberg matrix is also symmetric and thus tridiagonal, and so are all
QR_algorithm
Numerical methods for matrix eigenvalue calculation
stable algorithms for finding the eigenvalues of a matrix. These eigenvalue algorithms may also find eigenvectors. Given an n × n square matrix A of real
Eigenvalue_algorithm
Matrix with shifting rows
systems). The algorithms can also be used to find the determinant of a Toeplitz matrix in O ( n 2 ) {\displaystyle O(n^{2})} time. A Toeplitz matrix can also
Toeplitz_matrix
Matrix defined using smaller matrices called blocks
hence efficient solution algorithms for equation systems with a block tridiagonal matrix as coefficient matrix. The Thomas algorithm, used for efficient solution
Block_matrix
Gauss–Seidel method Tridiagonal matrix algorithm (Thomas algorithm): solves systems of tridiagonal equations SMAWK Algorithm Sparse matrix algorithms Cuthill–McKee
List_of_algorithms
Numerical eigenvalue calculation
resultant tridiagonal matrix may not be approximations to the original matrix. Therefore, the Lanczos algorithm is not very stable. Users of this algorithm must
Lanczos_algorithm
Matrix with non-zero elements only in a diagonal band
|i-j|>k} . A band matrix with k1 = k2 = 0 is a diagonal matrix, with bandwidth 0. A band matrix with k1 = k2 = 1 is a tridiagonal matrix, with bandwidth
Band_matrix
Matrix in which most of the elements are zero
1). For example, a tridiagonal matrix has lower bandwidth 1 and upper bandwidth 1. As another example, the following sparse matrix has lower and upper
Sparse_matrix
Special kind of square matrix
decomposition algorithm, an invertible matrix may be written as the product of a lower triangular matrix L and an upper triangular matrix U if and only
Triangular_matrix
Kind of square matrix in linear algebra
Hessenberg matrix at MathWorld. Hessenberg matrix at PlanetMath. High performance algorithms for reduction to condensed (Hessenberg, tridiagonal, bidiagonal)
Hessenberg_matrix
Finite difference method for numerically solving parabolic differential equations
diffusion, the algebraic problem is tridiagonal and may be efficiently solved with the tridiagonal matrix algorithm, which gives a fast O ( N ) {\displaystyle
Crank–Nicolson_method
Iterative method for solving the Sylvester matrix equations
involved is symmetric and tridiagonal (banded with bandwidth 3), and is typically solved using tridiagonal matrix algorithm. It can be shown that this
Alternating-direction implicit method
Alternating-direction_implicit_method
1016/j.laa.2006.09.008. S2CID 122729700. High performance algorithms for reduction to condensed (Hessenberg, tridiagonal, bidiagonal) form v t e v t e
Bidiagonal_matrix
Square matrix containing the distances between elements in a set
diagonalized distance matrix which is easily resolved by implementing the Householder tridiagonal-QL algorithm that takes in a distance matrix and returns the
Distance_matrix
Concept in linear algebra
tridiagonal and symmetric matrix is formed. In this example, also from Burden and Faires, the given matrix is transformed to the similar tridiagonal matrix
Householder_transformation
Mixture of several programming languages in the same program
Karmarkar's algorithm Particle swarm optimization Stone method Successive over-relaxation Symbolic Cholesky decomposition Tridiagonal matrix algorithm DAT10603
Pidgin_code
Topics referred to by the same term
analogue Time-division multiple access, a channel-access scheme Tridiagonal matrix algorithm, a mathematical system Digital AMPS (IS-54 and IS-136), a 2G
TDMA
Algorithm on Hermitian matrices
eigenvalue algorithms for Hermitian matrices, divide-and-conquer begins with a reduction to tridiagonal form. For an m × m {\displaystyle m\times m} matrix, the
Divide-and-conquer eigenvalue algorithm
Divide-and-conquer_eigenvalue_algorithm
Linear operator
also known as Jacobi matrix, is a symmetric linear operator acting on sequences which is given by an infinite tridiagonal matrix. It is commonly used
Jacobi_operator
Matrix-valued random variable
\neq 1,2,4} using the Dumitriu-Edelman tridiagonal trick. These are called the beta ensembles. Invariant matrix ensembles are random Hermitian matrices
Random_matrix
Algorithm for inverting a matrix
Rybicki-Press observation is that the matrix inverse of such a matrix is always a tridiagonal matrix (a matrix with nonzero entries only on the main diagonal
Rybicki_Press_algorithm
properties of a parallel Givens rotations-based solver for tridiagonal systems. A version of the algorithm, termed g-Spike, that is based on serial Givens rotations
SPIKE_algorithm
Stanley C. (1995). "A Divide-and-Conquer Algorithm for the Symmetric Tridiagonal Eigenproblem". SIAM Journal on Matrix Analysis and Applications. 16: 172–191
Arrowhead_matrix
numerical algorithms for linear algebra problems Types of matrices appearing in numerical analysis: Sparse matrix Band matrix Bidiagonal matrix Tridiagonal matrix
List of numerical analysis topics
List_of_numerical_analysis_topics
Numerical analysis concept
symmetric tridiagonal matrix. The QR algorithm is used to find the eigenvalues of this matrix. By taking advantage of the symmetric tridiagonal structure
Gauss–Legendre_quadrature
Square root of the determinant of a skew-symmetric square matrix
end{bmatrix}}=af-be+dc.} The Pfaffian of a 2n × 2n skew-symmetric tridiagonal matrix is given as pf [ 0 a 1 0 0 − a 1 0 0 0 0 0 0 a 2 0 0 − a 2 0 ⋱ ⋱
Pfaffian
off-diagonal entries of an n×n real symmetric matrix, A. It is the core operation in the Jacobi eigenvalue algorithm, which is numerically stable and well-suited
Jacobi_rotation
Triangular matrix Tridiagonal matrix Block matrix Sparse matrix Hessenberg matrix Hessian matrix Vandermonde matrix Stochastic matrix Toeplitz matrix Circulant
Outline_of_linear_algebra
real symmetric, real symmetric banded, real symmetric tridiagonal, special real tridiagonal, generalized real, and generalized real symmetric matrices
EISPACK
C++ software for numerical linear algebra
library of algorithms for numerical linear algebra that solves systems of linear equations and eigenvalue problems. It supports various matrix classes for
LAPACK++
Approximation of the definite integral of a function
&0&1\end{bmatrix}}^{\mathsf {T}}} , and J is the following tridiagonal matrix, called the Jacobi matrix: J = [ a 0 1 0 ⋯ 0 b 1 a 1 1 ⋱ ⋮ 0 b 2 ⋱ ⋱ 0 ⋮ ⋱ ⋱ a
Gaussian_quadrature
Mathematical algorithm
it might be wise to bring the matrix to the upper Hessenberg form first (for symmetric matrix this will be tridiagonal form). Which costs 10 3 n 3 + O
Inverse_iteration
libraries with significant linear algebra coverage. Matrix types (special types like bidiagonal/tridiagonal are not listed): Real – general (nonsymmetric)
Comparison of linear algebra libraries
Comparison_of_linear_algebra_libraries
Software library for numerical linear algebra
the data type. mm is a two-letter code denoting the kind of matrix expected by the algorithm. The codes for the different kind of matrices are reported
LAPACK
Method of analysis in probability theory
students starting around 1975." The method requires a transition rate matrix with tridiagonal block structure as follows Q = ( B 00 B 01 B 10 A 1 A 2 A 0 A 1
Matrix_geometric_method
Topics referred to by the same term
matrix and determinant of a smooth map between Euclidean spaces or smooth manifolds Jacobi operator (Jacobi matrix), a tridiagonal symmetric matrix appearing
Jacobi
Vector satisfying some of the criteria of an eigenvector
algebra, a generalized eigenvector of an n × n {\displaystyle n\times n} matrix A {\displaystyle A} is a vector which satisfies certain criteria which are
Generalized_eigenvector
Random matrix with gaussian entries
shift-invert Lanczos algorithm on the 10 n 1 / 3 × 10 n 1 / 3 {\displaystyle 10n^{1/3}\times 10n^{1/3}} upper left corner of the tridiagonal matrix form. From ordered
Gaussian_ensemble
equations can be solved using the modified tridiagonal matrix algorithm, also known as the Thomas algorithm. Under the condition of shock wave, dissipation
Beam_and_Warming_scheme
fast solvers for Poisson's equation express the problem as solving a tridiagonal matrix, discretising the solution on a regular grid. Systems which have good
Cyclic_reduction
Finite difference equation
Because [ A ] {\displaystyle {\begin{bmatrix}A\end{bmatrix}}} is block tridiagonal and sparse, many methods of solution have been developed to optimally
Discrete_Poisson_equation
Article title A Parallel Divide and Conquer Algorithm for the Generalized Real Symmetric Definite Tridiagonal Eigenproblem, C.F. Borges and W.B.Gragg, 1992
William_B._Gragg
real symmetric, real symmetric banded, real symmetric tridiagonal, special real tridiagonal, generalized real, and generalized real symmetric matices
List_of_numerical_libraries
American research center, 1985–1995
Bernard Philippe and Ahmed H. Sameh. “A Multiprocessor Algorithm for the Symmetric Tridiagonal Eigenvalue Problem”. SIAM Journal on Scientific and Statistical
University of Illinois Center for Supercomputing Research and Development
University_of_Illinois_Center_for_Supercomputing_Research_and_Development
Method of solving a linear system of equations
matrix A and the right-hand side vector B, employing the relaxation factor OMEGA, returning the calculated solution vector. --- The first algorithm step
Successive_over-relaxation
American mathematician (1932–2007)
and the SIAM Journal on Matrix Analysis and Applications (SIMAX). Golub, Gene H. (1962). "Bounds for eigenvalues of tridiagonal symmetric matrices computed
Gene_H._Golub
matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries
List_of_named_matrices
Indian-American mathematician and computer scientist
analysis and computational mathematics. His emphasis is on developing novel algorithms that respect the underlying problem structure and are scalable to large
Inderjit_Dhillon
NPB recognized that the benchmarks should feature new parallel-aware algorithmic and software methods, genericness and architecture neutrality, easy verifiability
NAS_Parallel_Benchmarks
{V}}_{i}^{\mathrm {T} }{\boldsymbol {AV}}_{i}} becomes symmetric and thus tridiagonal. It then can be more clearly denoted by H i = [ a 1 b 2 b 2 a 2 b 3 ⋱
Derivation of the conjugate gradient method
Derivation_of_the_conjugate_gradient_method
British applied mathematician (1932–2026)
solution of eigenvalue problems, the QR algorithm, the Lanczos algorithm, symmetric indefinite systems, and sparse matrix computations. Parlett died on February
Beresford_Parlett
Stanley C. (1995), "A divide-and-conquer algorithm for the symmetric tridiagonal eigenproblem", SIAM Journal on Matrix Analysis and Applications, 16 (1): 172–191
Simple_rational_approximation
Statistical experiment designs
internal counter is meaningless at the highest dose) - and it is not tridiagonal. Here is the expanded k {\displaystyle k} -in-a-row TPM with k = 2 {\displaystyle
Up-and-down_design
TRIDIAGONAL MATRIX-ALGORITHM
TRIDIAGONAL MATRIX-ALGORITHM
Female
German
Pet form of German Katarine, KATRIN means "pure."
Female
Finnish
Finnish form of Greek Margarites, MAARIT means "pearl."
Girl/Female
Maori
The Maori form of April.
Male
Hungarian
Czech and Hungarian form of Greek Patrikios, PATRIK means "patrician, of noble descent."
Male
French
French and German form of Greek Mattathias, MATHIS means "gift of God."
Female
English
English form of Latin Viatrix, BEATRIX means "voyager (through life)."
Male
English
Anglicized form of Irish Gaelic MainchÃn, MANNIX means "little monk."
Male
English
 English form of Roman Latin Martinus, MARTIN means "of/like Mars." Compare with another form of Martin.
Surname or Lastname
English (of Welsh origin)
English (of Welsh origin) : variant of Maddox.
Male
French
 French form of Roman Latin Martinus, MARTIN means "of/like Mars." Compare with another form of Martin.
Male
Italian
Italian form of Hebrew Mattithyah, MATTIA means "gift of God."
Female
Finnish
Finnish form of Greek Maria, MAARIA means "obstinacy, rebelliousness" or "their rebellion."Â
Girl/Female
Biblical
Rain, prison.
Female
Welsh
Welsh form of Old French Caterine, CATRIN means "pure."
Female
English
French form of Latin Maria, MARIE means "obstinacy, rebelliousness" or "their rebellion."
Female
English
Pet form of English Matilda, MATTIE means "mighty in battle." Compare with masculine Mattie.
Girl/Female
Arabic, Australian, Basque, French, Latin
Lady; Feminine of Martin; Warlike
Male
English
Pet form of English Martin, MARTIE means "of/like Mars."
Female
Finnish
Pet form of Finnish Katariina, KATRI means "pure."
Male
English
Pet form of English Matthew, MATTIE means "gift of God." Compare with feminine Mattie.
TRIDIAGONAL MATRIX-ALGORITHM
TRIDIAGONAL MATRIX-ALGORITHM
Boy/Male
Indian
Lord Vishnu
Girl/Female
American, Australian, Christian, French, Latin
Flower Name; Magnol's Flower
Boy/Male
English
Strong; open-minded. Blend of Jerold and Darell.
Boy/Male
Hindu
Lord Murugan, Always youth
Girl/Female
German, Teutonic
Famous Ruler
Female
Native American
Native American Hopi name PAVATI means "clear water."
Boy/Male
Arabic
Empty.
Boy/Male
American, Australian, British, English
Son of Ronald
Boy/Male
Indian, Telugu
Five Good Things
Surname or Lastname
English
English : variant of Oswald.
TRIDIAGONAL MATRIX-ALGORITHM
TRIDIAGONAL MATRIX-ALGORITHM
TRIDIAGONAL MATRIX-ALGORITHM
TRIDIAGONAL MATRIX-ALGORITHM
TRIDIAGONAL MATRIX-ALGORITHM
n.
In type founding and forging, an impression or matrix, formed by a punch drift.
n.
A housekeeper; esp., a woman who manages the domestic economy of a public instution; a head nurse in a hospital; as, the matron of a school or hospital.
n.
The cavity in which anything is formed, and which gives it shape; a die; a mold, as for the face of a type.
pl.
of Maori
n.
A rectangular arrangement of symbols in rows and columns. The symbols may express quantities or operations.
n.
The earthy or stony substance in which metallic ores or crystallized minerals are found; the gangue.
a.
Of or pertaining to the meter as a standard of measurement; of or pertaining to the decimal system of measurement of which a meter is the unit; as, the metric system; a metric measurement.
v. t.
The white fibrous matter forming the matrix from which fungi.
n.
The womb.
n.
A genus of swallows including the purple martin. See Martin.
n.
A mold; a matrix.
n.
Hence, that which gives form or origin to anything
pl.
of Matrix
v. i.
The mineral substance which incloses a vein; a matrix; a gangue.
n.
The lifeless portion of tissue, either animal or vegetable, situated between the cells; the intercellular substance.
n.
The five simple colors, black, white, blue, red, and yellow, of which all the rest are composed.
n.
See Matrix.
a.
Of or pertaining to the Maoris or to their language.
n.
The martin.