Software for weighted structured low-rank approximation

A software package is presented that computes locally optimal solutions to low-rank approximation problems with the following features: •mosaic Hankel structure constraint on the approximating matrix,•weighted 2-norm approximation criterion,•fixed elements in the approximating matrix,•missing elements in the data matrix, and•linear constraints on an approximating matrix’s left kernel basis. It implements a variable projection type algorithm and allows the user to choose standard local optimization methods for the solution of the parameter optimization problem. For an m×nm×n data matrix, with n>mn>m, the computational complexity of the cost function and derivative evaluation is  O(m2n)O(m2n). The package is suitable for applications with n≫mn≫m. In statistical estimation and data modeling–the main application areas of the package–n≫mn≫m corresponds to modeling of large amount of data by a low-complexity model. Performance results on benchmark system identification problems from the database DAISY and approximate common divisor problems are presented.