This self-contained introduction to numerical linear algebra provides a comprehensive, yet concise, overview of the subject. It includes standard material such as direct methods for solving linear systems and least-squares problems, error, stability and conditioning, basic iterative methods and the calculation of eigenvalues. Later chapters cover more advanced material, such as Krylov subspace methods, multigrid methods, domain decomposition methods, multipole expansions, hierarchical matrices and compressed sensing. The book provides rigorous mathematical proofs throughout, and gives algorithms in general-purpose language-independent form. Requiring only a solid knowledge in linear algebra and basic analysis, this book will be useful for applied mathematicians, engineers, computer scientists, and all those interested in efficiently solving linear problems.
This self-contained introduction to numerical linear algebra provides a comprehensive, yet concise, overview of the subject. It includes standard material such as direct methods for solving linear systems and least-squares problems, error, stability and conditioning, basic iterative methods and the calculation of eigenvalues. Later chapters cover more advanced material, such as Krylov subspace methods, multigrid methods, domain decomposition methods, multipole expansions, hierarchical matrices and compressed sensing. The book provides rigorous mathematical proofs throughout, and gives algorithms in general-purpose language-independent form. Requiring only a solid knowledge in linear algebra and basic analysis, this book will be useful for applied mathematicians, engineers, computer scientists, and all those interested in efficiently solving linear problems.
Stroll through medieval squares past soaring bell towers and along quiet canals: with Rick Steves on your side, Belgium can be yours!Inside Rick Steves Belgium: Bruges, Brussels, Antwerp & Ghent y
Give simple quilt blocks a touch of magic - the add-a-strip way! Start with simple squares, triangles, and diamonds, then slice and insert a 1" strip of contrasting fabric to create dozens of new
The game of Dots-and-Boxes, the popular game in which two players take turns connecting an array of dots to form squares, or "boxes" has long been considered merely a child's game. In this book, howev
5952 3 Times the Charm, Book 2: An exciting encore to the original best-seller from Me and My Sister Designs, this book presents 21 easy little quilts featuring charm squares, with 7 new designs each
This is a biography of Earthopolis, the only Urban Planet we know of. It is a history of how cities gave humans immense power over Earth, for good and for ill. Carl Nightingale takes readers on a sweeping six-continent, six-millennia tour of the world's cities, culminating in the last 250 years, when we vastly accelerated our planetary realms of action, habitat, and impact, courting dangerous new consequences and opening prospects for new hope. In Earthopolis we peek into our cities' homes, neighborhoods, streets, shops, eating houses, squares, marketplaces, religious sites, schools, universities, offices, monuments, docklands, and airports to discover connections between small spaces and the largest things we have built. The book exposes the Urban Planet's deep inequalities of power, wealth, access to knowledge, class, race, gender, sexuality, religion and nation. It asks us to draw on the most just and democratic moments of Earthopolis's past to rescue its future.
San Antonio was founded in 1718. By 1730, the viceroy of New Spain had issued orders to map plazas, squares, and parks for the Canary Islanders who would be arriving in 1731. The plazas with their mar
Quasi-interpolation is one of the most useful and often applied methods for the approximation of functions and data in mathematics and applications. Its advantages are manifold: quasi-interpolants are able to approximate in any number of dimensions, they are efficient and relatively easy to formulate for scattered and meshed nodes and for any number of data. This book provides an introduction into the field for graduate students and researchers, outlining all the mathematical background and methods of implementation. The mathematical analysis of quasi-interpolation is given in three directions, namely on the basis (spline spaces, radial basis functions) from which the approximation is taken, on the form and computation of the quasi-interpolants (point evaluations, averages, least squares), and on the mathematical properties (existence, locality, convergence questions, precision). Learn which type of quasi-interpolation to use in different contexts and how to optimise its features to su
This Element discusses how shiny, an R package, can help instructors teach quantitative methods more effectively by way of interactive web apps. The interactivity increases instructors' effectiveness by making students more active participants in the learning process, allowing them to engage with otherwise complex material in an accessible, dynamic way. The Element offers four detailed apps that cover two fundamental linear regression topics: estimation methods (least squares, maximum likelihood) and the classic linear regression assumptions. It includes a summary of what the apps can be used to demonstrate, detailed descriptions of the apps' full capabilities, vignettes from actual class use, and example activities. Two other apps pertain to a more advanced topic (LASSO), with similar supporting material. For instructors interested in modifying the apps, the Element also documents the main apps' general code structure, highlights some of the more likely modifications, and goes through
Joseph Liouville is recognised as one of the great mathematicians of the nineteenth century, and one of his greatest achievements was the introduction of a powerful new method into elementary number theory. This book provides a gentle introduction to this method, explaining it in a clear and straightforward manner. The many applications provided include applications to sums of squares, sums of triangular numbers, recurrence relations for divisor functions, convolution sums involving the divisor functions, and many others. All of the topics discussed have a rich history dating back to Euler, Jacobi, Dirichlet, Ramanujan and others, and they continue to be the subject of current mathematical research. Williams places the results in their historical and contemporary contexts, making the connection between Liouville's ideas and modern theory. This is the only book in English entirely devoted to the subject and is thus an extremely valuable resource for both students and researchers alike.
Chess, one of the world’s most popular games, has inspired artists for hundreds of years. Though apparently offering a limited canvas – each set has 32 pieces, each board 64 squares – sets have nevert
This book, first published in 1991, is devoted to the exposition of combinatorial matrix theory. This subject concerns itself with the use of matrix theory and linear algebra in proving results in combinatorics (and vice versa), and with the intrinsic properties of matrices viewed as arrays of numbers rather than algebraic objects in themselves. There are chapters dealing with the many connections between matrices, graphs, digraphs and bipartite graphs. The basic theory of network flows is developed in order to obtain existence theorems for matrices with prescribed combinatorial properties and to obtain various matrix decomposition theorems. Other chapters cover the permanent of a matrix, and Latin squares. The final chapter deals with algebraic characterizations of combinatorial properties and the use of combinatorial arguments in proving classical algebraic theorems, including the Cayley-Hamilton Theorem and the Jordan Canonical Form. The book is sufficiently self-contained for use
Quantile regression is gradually emerging as a unified statistical methodology for estimating models of conditional quantile functions. By complementing the exclusive focus of classical least squares regression on the conditional mean, quantile regression offers a systematic strategy for examining how covariates influence the location, scale and shape of the entire response distribution. This monograph is the first comprehensive treatment of the subject, encompassing models that are linear and nonlinear, parametric and nonparametric. The author has devoted more than 25 years of research to this topic. The methods in the analysis are illustrated with a variety of applications from economics, biology, ecology and finance. The treatment will find its core audiences in econometrics, statistics, and applied mathematics in addition to the disciplines cited above.
Perfect for high-energy story times, this cumulative tale is a madcap mash-up featuring robots, shapes in motley amalgamation, and . . . pie!Squares, rectangles, ovals, triangles, and other colorful s
Whenever you are -- inside or outside -- there are shapes to discover. And with Tana Hoban's help you will begin to see them. Look around. How many circles, squares, stars, triangles, hearts, and rec
Because of their intuitive layout, extensive mathematical capabilities, and convenient graphics, spreadsheets provide an easy, straightforward route to scientific computing. This textbook for undergraduate and entry-level graduate chemistry and chemical engineering students uses Excel, the most powerful available spreadsheet, to explore and solve problems in general and chemical data analysis. This is the only up-to-date text on the use of spreadsheets in chemistry. The book discusses topics including statistics, chemical equilibria, pH calculations, titrations, and instrumental methods such as chromatography, spectrometry, and electroanalysis. It contains many examples of data analysis, and uses spreadsheets for numerical simulations, and testing analytical procedures. It also treats modern data analysis methods such as linear and non-linear least squares in great detail, as well as methods based on Fourier transformation. The book shows how matrix methods can be powerful tools in dat
The hotly anticipated follow-up to The Piranhas, the bestselling novel and major motion pictureNicolas Fiorillo and his gang of children―his paranza―control the squares of Forcella after their rapid r
Anchored around the county seat of Jasper with a population of less than 500 and one of the most picturesque courthouse squares in the state, Newton County is a nature lover's dream. The majority of t
