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Structured Matrix Based Methods for Approximate Polynomial GCD
Defining and computing a greatest common divisor of two polynomials with inexact coefficients is a classical problem in symbolic-numeric computation. The first part of this book reviews the main results that have been proposed so far in the literature. As usual with polynomial computations, the polynomial GCD problem can be expressed in matrix form: the second part of the book focuses on this point of view and analyses the structure of the relevant matrices, such as Toeplitz, Toepliz-block and displacement structures. New algorithms for the computation of approximate polynomial GCD are presented, along with extensive numerical tests. The use of matrix structure allows, in particular, to lower the asymptotic computational cost from cubic to quadratic order with respect to polynomial degree.
Numerical Methods for Structured Matrices and Applications
This cross-disciplinary volume brings together theoretical mathematicians, engineers and numerical analysts and publishes surveys and research articles related to topics such as fast algorithms, in which the late Georg Heinig made outstanding achievements.
A Journey through the History of Numerical Linear Algebra
This expansive volume describes the history of numerical methods proposed for solving linear algebra problems, from antiquity to the present day. The authors focus on methods for linear systems of equations and eigenvalue problems and describe the interplay between numerical methods and the computing tools available at the time. The second part of the book consists of 78 biographies of important contributors to the field. A Journey through the History of Numerical Linear Algebra will be of special interest to applied mathematicians, especially researchers in numerical linear algebra, people involved in scientific computing, and historians of mathematics.
Separable Type Representations of Matrices and Fast Algorithms
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 first volume consists of four parts. The first part is of a mainly theoretical character introducing and studying the quasiseparable and semiseparable representations of matrices and minimal rank completion problems. Three furt...
Computer Algebra in Scientific Computing
This book constitutes the proceedings of the 18th International Workshop on Computer Algebra in Scientific Computing, CASC 2016, held in Bucharest, Romania, in September 2016. The 32 papers presented in this volume were carefully reviewed and selected from 39 submissions. They deal with cutting-edge research in all major disciplines of Computer Algebra.
Recent Advances in Real Complexity and Computation
This volume is composed of six contributions derived from the lectures given during the UIMP-RSME Lluis Santalo Summer School on ``Recent Advances in Real Complexity and Computation'', held July 16-20, 2012, in Santander, Spain. The goal of this Summer School was to present some of the recent advances on Smale's 17th Problem: ``Can a zero of $n$ complex polynomial equations in $n$ unknowns be found approximately, on the average, in polynomial time with a uniform algorithm?'' These papers cover several aspects of this problem: from numerical to symbolic methods in polynomial equation solving, computational complexity aspects (both worse and average cases and both upper and lower complexity bounds) as well as aspects of the underlying geometry of the problem. Some of the contributions also deal with either real or multiple solutions solving.
Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications
Focusing on special matrices and matrices which are in some sense `near’ to structured matrices, this volume covers a broad range of topics of current interest in numerical linear algebra. Exploitation of these less obvious structural properties can be of great importance in the design of efficient numerical methods, for example algorithms for matrices with low-rank block structure, matrices with decay, and structured tensor computations. Applications range from quantum chemistry to queuing theory. Structured matrices arise frequently in applications. Examples include banded and sparse matrices, Toeplitz-type matrices, and matrices with semi-separable or quasi-separable structure, as well as Hamiltonian and symplectic matrices. The associated literature is enormous, and many efficient algorithms have been developed for solving problems involving such matrices. The text arose from a C.I.M.E. course held in Cetraro (Italy) in June 2015 which aimed to present this fast growing field to young researchers, exploiting the expertise of five leading lecturers with different theoretical and application perspectives.
Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation
This book contains a collection of research articles and surveys on recent developments on operator theory as well as its applications covered in the IWOTA 2011 conference held at Sevilla University in the summer of 2011. The topics include spectral theory, differential operators, integral operators, composition operators, Toeplitz operators, and more. The book also presents a large number of techniques in operator theory.
Birth and Death of the Housewife
Stepping out of her beloved trunk full of bread crumbs, dust, spider webs, books, and ragged funeral ornaments, the young protagonist of Paola Masino's most controversial novel realizes that her fate is already sealed. She will have to conform to society's expectations of a woman: her wild imagination will have to be controlled, her intelligence kept at bay. In short, she will have to become a Housewife. Subject to Fascist censorship before its first publication in 1945, Birth and Death of the Housewife offers a surrealist criticism of Fascism and the rigid notion of womanhood it promoted. In her depiction of a woman's struggle to play a role that simply does not correspond to her desires, Masino expresses a frustration and a rebellious instinct rarely found among her contemporaries. Defying interpretations and standing alone among the heroines of twentieth-century Italian literature, Masino's Housewife remains an uncomfortable, enigmatic figure whose impudent determination to challenge the bulwarks of traditional female roles reaches beyond historical boundaries and resonates powerfully with contemporary readers.
Contemporary Italian Women Writers and Traces of the Fantastic
Contemporary fantastic fiction, particularly that written by women, often challenges traditional literary practice. At the same time the predominantly male-authored canon of fantastic literature offers a problematic range of gender stereotypes for female authors to 're-write'.
