Introduction The three basic problems we will address in this book are as follows. In all cases we are given as data a matrix A ∈ C m×n , with m ≥ n and, for the rst two problems, the vector b ∈ C m. (SLE) denotes simultaneous linear equations, (LSQ) denotes least squares and (EVP) denotes eigenvalue problem.

Many tasks require finding groups of elements in a matrix of numbers, symbols or class likelihoods. One approach is to use efficient bior tri-linear factorization techniques including PCA, ICA, sparse matrix factorization and plaid analysis. These techniques are not appropriate when addition and multiplication of matrix elements are not sensibly defined. More directly, methods like biclustering...