This two-volume work presents a systematic theoretical and
computational study of several types of generalizations of
separable matrices. The main attention is paid to fast algorithms
(many of linear complexity) for matrices in semiseparable,
quasiseparable, band and companion form. The work is focused on
algorithms of multiplication, inversion and description of
eigenstructure and includes a large number of illustrative examples
throughout the different chapters.
The second volume, consisting of four parts, addresses the
eigenvalue problem for matrices with quasiseparable structure and
applications to the polynomial root finding problem. In the first
part the properties of the characteristic polynomials of principal
leading submatrices, the structure of eigenspaces and the basic
methods to compute eigenvalues are studied in detail for matrices
with quasiseparable representation of the first order. The second
part is devoted to the divide and conquer method, with the main
algorithms being derived also for matrices with quasiseparable
representation of order one. The QR iteration method for some
classes of matrices with quasiseparable of any order
representations is studied in the third part. This method is then
used in the last part in order to get a fast solver for the
polynomial root finding problem. The work is based mostly on
results obtained by the authors and their coauthors. Due to its
many significant applications and the accessible style the text
will be useful to engineers, scientists, numerical analysts,
computer scientists and mathematicians alike.
General
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