FAST BLOCK DIAGONALIZATION OF $(k,k')$-PENTADIAGONAL MATRICES

Abstract

In this paper, we provide a block diagonalization algorithm of (k, k ′ )-pentadiagonal matrices. The algorithm is a structure-preserving algorithm in that the small diagonal blocks essentially have the same nonzero structure as the original one, and it can be regarded as an extension of the block diagonalization algorithm of k-tridiagonal matrices in [T. Sogabe,

Bioengineering Considerations for a Nurturing Way to Enhance Scalable Expansion of Human Pluripotent Stem Cells

“…The Rho/Rho kinase signaling pathway regulates the sensitivity of cells to mechanical stimuli. [78][79][80][81] For example, RhoA phosphorylates Rho-associated coiled-coil kinase (ROCK), which activates non-muscle myosin II contractility by phosphorylation of myosin regulatory light chain (MLC). This increased contractility stimulates nuclear translocation of transcription regulators such as -catenin (WNT effector), Yes-associated protein (YAP), and transcriptional coactivator with PDZ-binding motif (TAZ), and thereby influences cellular mechanoresponses.…”

Bidiagonalization of (k, k + 1)-tridiagonal matrices

“…These matrices are related to k-Hessenberg matrices Hn(k) [2], in that T (k,k+ ) n with k = corresponds to Hn(k) with k = , and can be regarded as a variant of k-tridiagonal matrices (see, e.g., [1,7]). Moreover, a (k, k + )-tridiagonal matrix is a special case of a (k, k )-pentadiagonal matrix (see, e.g., [6]). In fact, if k = k + , and the k-th superdiagonal and k -th subdiagonal are all zero, then a (k, k )pentadiagonal matrix is a (k, k + )-tridiagonal matrix.…”

“…In fact, if k = k + , and the k-th superdiagonal and k -th subdiagonal are all zero, then a (k, k )pentadiagonal matrix is a (k, k + )-tridiagonal matrix. For k-tridiagonal matrices and (k, k )-pentadiagonal matrices, the fast block diagonalization algorithm using a permutation matrix is discussed in [6,7]. However, the (k, k + )-tridiagonal matrices are irreducible in the sense that the block size of the matrix produced by the block diagonalization algorithm in [6] is one.…”