In linear algebra, a tridiagonal matrix is a band matrix that has nonzero elements only on the main diagonal, the subdiagonal/lower diagonal (the first...

In numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas), is a simplified form...

block tridiagonal matrix as coefficient matrix. The Thomas algorithm, used for efficient solution of equation systems involving a tridiagonal matrix can...

In linear algebra, a Toeplitz matrix or diagonal-constant matrix, named after Otto Toeplitz, is a matrix in which each descending diagonal from left to...

|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...

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...

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...

tridiagonal and symmetric matrix is formed. In this example, also from Burden and Faires, the given matrix is transformed to the similar tridiagonal matrix...

Multiplication operator Tridiagonal matrix Toeplitz matrix Toral Lie algebra Circulant matrix Proof: given the elementary matrix e i j {\displaystyle e_{ij}}...

elimination QR decomposition Cholesky decomposition Hessenberg matrix Tridiagonal matrix Invariant subspace Axler, Sheldon Jay (1997). Linear Algebra Done...

continuant is a multivariate polynomial representing the determinant of a tridiagonal matrix and having applications in continued fractions. The n-th continuant...

upper Hessenberg. A matrix that is both upper Hessenberg and lower Hessenberg is a tridiagonal matrix, of which the Jacobi matrix is an important example...

of exact inertia and inclusions of eigenvalues (singular values) of tridiagonal (bidiagonal) matrices". Linear Algebra and Its Applications. 422 (1):...

QR algorithm. If the original matrix is symmetric, then the upper Hessenberg matrix is also symmetric and thus tridiagonal, and so are all the Ak. In this...

spaces or smooth manifolds Jacobi operator (Jacobi matrix), a tridiagonal symmetric matrix appearing in the theory of orthogonal polynomials This disambiguation...

matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries...

linear diffusion, the algebraic problem is tridiagonal and may be efficiently solved with the tridiagonal matrix algorithm, which gives a fast O ( N ) {\displaystyle...

symmetric tridiagonal matrix. The QR algorithm is used to find the eigenvalues of this matrix. By taking advantage of the symmetric tridiagonal structure...

matrix may be needed to transform the eigenvectors of the Hessenberg matrix back into eigenvectors of the original matrix. For symmetric tridiagonal eigenvalue...

value decomposition. It also includes routines to implement the associated matrix factorizations such as LU, QR, Cholesky and Schur decomposition. LAPACK...

divide-and-conquer begins with a reduction to tridiagonal form. For an m × m {\displaystyle m\times m} matrix, the standard method for this, via Householder...

&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...

analysis: Sparse matrix Band matrix Bidiagonal matrix Tridiagonal matrix Pentadiagonal matrix Skyline matrix Circulant matrix Triangular matrix Diagonally dominant...

and which represents a symmetric, tridiagonal matrix. For an equidistant grid one gets a Toeplitz matrix. The 2D case shows all the characteristics...

m {\displaystyle n\times m} matrix V {\displaystyle V} with orthonormal columns and a tridiagonal real symmetric matrix T = V ∗ A V {\displaystyle T=V^{*}AV}...

Karmarkar's algorithm Particle swarm optimization Stone method Successive over-relaxation Symbolic Cholesky decomposition Tridiagonal matrix algorithm...

Triangular matrix Tridiagonal matrix Block matrix Sparse matrix Hessenberg matrix Hessian matrix Vandermonde matrix Stochastic matrix Toeplitz matrix Circulant...

MDMA analogue Time-division multiple access, a channel-access scheme Tridiagonal matrix algorithm, a mathematical system Digital AMPS (IS-54 and IS-136),...

off-tridiagonal cell individually in a medium to large matrix. However, if Jacobian rotations are repeatedly performed on the above-tridiagonal cell...

diagonalized distance matrix which is easily resolved by implementing the Householder tridiagonal-QL algorithm that takes in a distance matrix and returns the...