Showing papers on "Tridiagonal matrix algorithm published in 1972"
31 citations
TL;DR: The algorithm presented here works by eliminating all off-diagonal variables in terms of the diagonal ones, and then specifying values for the diagonal variables for tridiagonal problems in n steps for an n-origin, n-destination problem.
Abstract: Some transportation problems are such that, when origins and destinations are suitably indexed, the cost matrix contains elements along the main diagonal, a band above it, and a band below it, whil...
15 citations
Abstract: This paper presents an algorithm for finding the eigenvalues of tridiagonal symmetric matrices. The method is in fact Laguerre's method modified in such a way that the explicit calculations of the coefficients of characteristic polynomial are avoided. Each eigenvalue is evaluated by the iterative process with cubic rate of convergence.
9 citations
TL;DR: A cost criterion function for choosing the optimal pivot at each stage of the Gaussian elimination method is described, which takes into consideration both the fill-in and the number of arithmetical operations.
Abstract: In this note, a cost criterion function for choosing the optimal pivot at each stage of the Gaussian elimination method is described It takes into consideration both the fill-in and the number of arithmetical operations Other known criterion functions byTewarson [4] andMarkowitz [6] are also discussed and compared with the new criterion function
4 citations
TL;DR: In general, for large values of Nn the problem of determining the eigenvalues and eigenvectors can only be solved by extensive calculation, and some problems involving the approximation of linear second order partial differential equations in two independent variables by difference equations lead to block tridiagonal coefficient matrices M.
Abstract: Let M be a square matrix of order Nn. Partition M into N 2 square matrices M(A, B), 1 < A, B < N, of order n; and let M(A, B; i , j ) , 1 < i,j < n, denote the element in the ith row and j th column o f M ( A , B). In general, for large values of Nn the problem of determining the eigenvalues and eigenvectors can only be solved by extensive calculation. For special classes of matrices M, of the type we shall consider, the eigenvalues and eigenvectors can be found explicitly• To motivate our specialization we remark that some problems involving the approximation of linear second order partial differential equations in two independent variables by difference equations lead to block tridiagonal coefficient matrices M, i.e. M(A,B) = 0 when [A -B] > 1. In particular, if the partial differential equation being approximated has constant coefficients, one may have
1 citations
1 Sep 1972
TL;DR: In this paper, the closed form inverse of a fairly general tridiagonal matrix is given, where the restriction is that the off-diagonal elements in the tridagonal band be nonzero.
Abstract: : The closed form inverse of a fairly general tridiagonal matrix is given. The restriction is that the off-diagonal elements in the tridiagonal band be nonzero. If the elements of the matrix are integers, where the upper off-diagonal elements are equal and the lower off-diagonal elements are equal, then an integer multiple of each element of the inverse can be generated by integer arithmetic.