This two-volume paintings provides a scientific theoretical and computational learn of different types of generalizations of separable matrices. the most cognizance is paid to speedy algorithms (many of linear complexity) for matrices in semiseparable, quasiseparable, band and spouse shape. The paintings is targeted on algorithms of multiplication, inversion and outline of eigenstructure and features a huge variety of illustrative examples during the assorted chapters.

The moment quantity, along with 4 components, addresses the eigenvalue challenge for matrices with quasiseparable constitution and purposes to the polynomial root discovering challenge. within the first half the homes of the attribute polynomials of significant prime submatrices, the constitution of eigenspaces and the elemental how to compute eigenvalues are studied intimately for matrices with quasiseparable illustration of the 1st order. the second one half is dedicated to the divide and overcome strategy, with the most algorithms being derived additionally for matrices with quasiseparable illustration of order one. The QR generation technique for a few periods of matrices with quasiseparable of any order representations is studied within the 3rd half. this system is then utilized in the final half which will get a quick solver for the polynomial root discovering challenge. The paintings is primarily based on effects acquired by means of the authors and their coauthors. because of its many major functions and the available type the textual content may be worthy to engineers, scientists, numerical analysts, machine scientists and mathematicians alike.