Eigendecomposition of Block Tridiagonal Matrices

摘要: Block tridiagonal matrices arise in applied mathematics, physics, and signal processing. Many applications require knowledge of eigenvalues eigenvectors block matrices, which can be prohibitively expensive for large matrix sizes. In this paper, we address the problem eigendecomposition by studying a connection between their zeros appropriate polynomials. We use with polynomials to derive closed-form expression eliminates need direct calculation lead faster eigenvalues. also demonstrate an example that our work fast algorithms eigenvector expansion matrices.