Tridiagonal matrix algorithm

Abstract: Modification of Potter method of Gaussian elimination for solving eigenvalue problems of buckling and free vibrations of shells of revolution

Abstract: The dynamics of relativistic atomic wave functions evolving under the influence of intense laser pulses is used as an example of a general class of applications employing the alternating direction implicit method. The method requires the solution of many tridiagonal systems of linear equations. A range of parallel algorithms for this setting are analyzed with respect to their scalability on large parallel machines.

Abstract: Olver has given an elegant construction of recessive solutions of nonhomogeneous scalar three term recurrence relations. We investigate the feasibility of applying his methods to block tridiagonal nonhomogeneous systems where the coefficient matrices A B C are n × n matrices and Y and D are n × m. Such systems with m = 1 arise in numerical methods for solving partial differential equations [7,11]. Of course, the results obtained are also applicable to the symmetric case with and symmetric Bk . The homogeneous case with m = n arises in matrix continued fractions [4] and the well-studied symmetric homogeneous case is closely realted to discrete Hamiltonian systems and, for m = n, to discrete Riccati equations [2,1,3,5].

Abstract: For the tridiagonal system of linear algebraic equations whose matrix is nonstrictly Jacobi diagonally dominant in columns we establish sufficient conditions for all components of the solution to be nonnegative.