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Petronilho, Eigenproblem for tridiagonal 2-Toeplitz matrices and quadratic polynomial mappings, Linear Alg.
Since the matrix A is symmetric and tridiagonal, advancing the solution by one time step requires only O(N) operations.
On subsequent iterations one calculates only residual matrix solving the two tridiagonal systems.
The implicit solution scheme of equations (10)-(15) was solved using a tridiagonal matrix algorithm (Thomas algorithm) programmed in Matlab[R].
v] correspond to eigenvectors of a certain tridiagonal matrix obtained from the Legendre differential equation.
In the case of generalized Birth and Death process the system matrix is of tridiagonal structure and the transitions are mapped by the following matrix for production chain of identical machines of parameters k=5, m=3, r=3, i.
Equation (15) is a tridiagonal system of linear equations, which can be solved efficiently using Thomas Agorithm [21].
Essas aproximacoes transformam o problema de equacao diferencial em um sistema tridiagonal de equacoes lineares que, a cada instante, deve ser resolvido para gerar a temperatura proxima ao centro das frutas; para tanto, uma estimativa do valor de hc deve ser inserida no modelo, sendo todos os outros valores de parametros tomados com os ja referidos.
The inverse of the covariance matrix to the proposal distribution has the convenient tridiagonal form:
The authors, an international trio of computer scientists and researchers in applied mathematics, provide case studies for each new concept as they introduce semiseparable and related matrices, focusing on definitions and properties, representation, and historical applications; linear systems with semiseparable and related matrices, including Gaussian elimination, the QR factorization, a Levinson-like and Schur-like solver, and inverting semiseparable and related matrices, including known factorizations, direct inversion methods, general formulas for inversions, scaling of symmetric positive definite semiseparable matrices and decay rates for the inverses of tridiagonal matrices.
Ng, 2001, Pricing Discrete Barrier and Hindsight Options With the Tridiagonal Probability Algorithm, Management Science, 47(3): 383-393.