In mathematics, particularly matrix theory, a band matrix or banded matrix is a sparse matrix whose non-zero entries are confined to a diagonal band, comprising the main diagonal and zero or more diagonals on either side.

In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices. [1][2]

Feb 24, 2016 · You will be able to do a symmetric permutation $PAP^T$ of each diagonal block $A$ into a block diagonal matrix with many small blocks on the main diagonal. Here $P$ is a permutation matrix. These small blocks will be banded and dense within the band.

Sep 15, 2014 · We compare different algorithms for computing eigenvalues and eigenvectors of a symmetric band matrix across a wide range of synthetic test problems.

A band matrix is a sparse matrix whose nonzero entries are confined to a diagonal band, consisting of the main diagonal and zero or more diagonals on either side. A tri- or bidiagonal matrix is a band matrix. Band matrices occur in applications, particularly when finding approximate solutions to partial differential equations.

Sep 15, 2022 · In this lecture, we will consider various types of sparse direct factorization methods. We’ll focus throughout on Cholesky, simply to avoid the awkward-ness associated with pivoting. We begin with the case of band matrices. The bandwidth b of a matrix is the smallest non-negative integer b such that aij = 0 for |i j > b.

The conclusion is that if the matrix A with L blocks per row(2 by 2 matrices R i ;S i ;:::) has a banded inverse, then A can factored recursively into a product of L 1 block bidiagonal matrices with rank-one blocks.

Let us consider a few different types of banded matrices. Figure 27.1: A banded matrix with bandwidth mb m b. Figure 27.2: A spring-mass system whose equilibrium state calculation gives rise to a pentadiagonal matrix.

ection II, we define the notation used to represent block-banded matrices and derive three important properties for -block-banded ma. rices. These properties express the block entries of an -block-banded ma-trix in terms of the block entries of its inverse, and vice.

In this paper, we study a band constrained nonnegative matrix factorization (band NMF) problem: for a given nonnegative matrix Y, decompose it as Y ≈ AX with A a nonnegative matrix and X a nonnegative block band matrix.