Block Locally Toeplitz Sequences: Construction and Properties

The theory of block locally Toeplitz (LT) sequences—along with its generalization known as the theory of block generalized locally Toeplitz (GLT) sequences—is a powerful apparatus for computing the spectral distribution of matrices arising from the discretization of differential problems. In this paper we develop the theory of block LT sequences, whereas the theory of block GLT sequences is the subject of the complementary paper (Chap. 3 of this book).