Episode March 3, 2026 20 min 27s

Matrix Computations and Semiseparable Matrices: Linear Systems

From Book Shelter Book Shelter

Explores the theory and application of structured rank matrices, with a particular focus on semiseparable and quasiseparable matrices. It details definitions and properties of various matrix classes, including their relationships, representations (such as Givens-vector and generator), and closure properties under operations like inversion. The source also examines numerical algorithms for these matrices, such as Gaussian elimination, QR-factorization, and Levinson-like solvers, alongside their applications in fields like statistics and integral equations, and discusses methods for computing eigenvalues and inverting structured rank matrices. Finally, it touches upon hierarchical matrices and provides a bibliography for further research and the SSPack software package.

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