Publisher: Birkhäuser; 2013 edition (October 10, 2013)
Format: PDF / Kindle / ePub
Size: 8.7 MB
Downloadable formats: PDF
This two-volume paintings provides a scientific theoretical and computational research of different types of generalizations of separable matrices. the first concentration is on quickly algorithms (many of linear complexity) for matrices in semiseparable, quasiseparable, band and significant other shape. The paintings examines algorithms of multiplication, inversion and outline of eigenstructure and contains a wealth of illustrative examples during the assorted chapters. the 1st quantity comprises 4 components. the 1st half is especially theoretical in personality, introducing and learning the quasiseparable and semiseparable representations of matrices and minimum rank finishing touch difficulties. 3 additional completions are handled within the moment half. the 1st functions of the quasiseparable and semiseparable constitution are integrated within the 3rd half, the place the interaction among the quasiseparable constitution and discrete time various linear structures with boundary stipulations play a vital position. The fourth half contains factorization and inversion speedy algorithms for matrices through quasiseparable and semiseparable buildings. The paintings is primarily based on effects acquired through the authors and their coauthors. because of its many major purposes and obtainable sort, the textual content can be a invaluable source for engineers, scientists, numerical analysts, laptop scientists and mathematicians alike. the second one quantity, which includes 4 components, addresses the eigenvalue challenge for matrices with quasiseparable constitution and functions to the polynomial root discovering challenge. within the first half the houses of the attribute polynomials of crucial best submatrices, the constitution of eigenspaces and the fundamental equipment for computing 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 additionally being derived for matrices with quasiseparable illustration of order one. The QR generation technique for a few periods of matrices with quasiseparable representations of any order is studied within the 3rd half. this technique is then utilized in the final half for you to supply a quick solver for the polynomial root discovering challenge. The paintings is primarily based on effects bought by way of the authors and their coauthors. as a result of its many major purposes and available type, the textual content could be a worthy source for engineers, scientists, numerical analysts, laptop scientists and mathematicians alike.