A tridiagonal matrix has nonzero elements only on the main diagonal, the diagonal upon the main diagonal, and the diagonal below the main diagonal. This special structure appears often in scientific computing and computer graphics [1, 2]. Because many of them require real-time execution, the ...
A matrix A=(aij)∈Mn(R) is said to be tridiagonal if aij=0 when |i−j|>1, that is, when it has the following structure:A=(a1b10c1a2b2c2⋱⋱⋱⋱bn−10cn−1an) Lemma 3.1 [6] Let the matrix A be defined as in (3.1). Then A is irreducible if and only if bici...
Block-tridiagonalmatrices：块三对角矩阵
The block tridiagonal structure is fully exploited; high data locality is achieved, which is important for high efficiency on modern computer systems; very little fill-in occurs, which leads to no or very low memory overhead; and in most practical situations observed the transformed matrix has ve...
Motivated by the structure of a matrix factorization introduced recently by Evans (1999), we introduce a new WZ factorization for use with the partition method for parallel solution of tridiagonal systems. The factorization helps us to uncouple partitioned subsystems for parallel processing of their ...
DATA transmission systemsCOMPUTER softwareIn the present paper, we mainly consider the direct solution of cyclic tridiagonal linear systems. By using the specific low-rank and Toeplitz-like structure, we derive a structure-preserving factorization of the coefficient matrix. Based on the combination of ...
The Toeplitz structure is destroyed since two elements on each off-diagonal are perturbed. Based on a careful analysis, we derive sharp bounds for the extremal eigenvalues of this class of matrices in terms of the original data of the given matrix. In this way, we also obtain a lower bound...
Research of graphics processing units (GPUs) provide a new idea for solving a tridiagonal matrix in parallel. Due to the limitations of GPU architecture and memory-access methods, the parallel execution of a tridiagonal matrix solver must break the inherent linear dependency of the equations. In ...
We say that x is g-tridiagonally majorized by y (written as x≺gty) if there exists a tridiagonal g-doubly stochastic matrix D∈Ωnt such that x=Dy. In [3], the authors found the structure of strong linear preservers of ≺gt on Rn as follows:...
The Toeplitz structure is destroyed since two elements on each off-diagonal are perturbed. Based on a careful analysis, we derive sharp bounds for the extremal eigenvalues of this class of matrices in terms of the original data of the given matrix. In this way, we also obtain a lower bound...