Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

"This book introduces a method of reasearch which can be used in various fields of mathematics. It examines, in a systematic way, the quantitative characterizations of the "deviation from a (given) property", called the "defect of a property", in: set theory; topology; measure theory; real, complex and functional analysis; algebra; geometry; number theory; fuzzy mathematics"--P. [2] of cover.

Mathematics. --- Fuzzy mathematics. --- Deviation (Mathematics) --- Defects (Mathematics) --- Error analysis (Mathematics) --- Mathematics --- Math --- Science --- Numerical analysis --- Deviation (Mathematics).

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Bootstrap (Statistics) --- Error analysis (Mathematics) --- Estimation theory. --- Forest surveys --- Forests and forestry --- Statistical methods. --- Estimation theory --- Internet resource --- Statistical methods --- Alaska, Southeast

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

In response to a growing interest in Total Least Squares (TLS) and Errors-In-Variables (EIV) modeling by researchers and practitioners, well-known experts from several disciplines were invited to prepare an overview paper and present it at the third international workshop on TLS and EIV modeling held in Leuven, Belgium, August 27-29, 2001. These invited papers, representing two-thirds of the book, together with a selection of other presented contributions yield a complete overview of the main scientific achievements since 1996 in TLS and Errors-In-Variables modeling. In this way, the book nicely completes two earlier books on TLS (SIAM 1991 and 1997). Not only computational issues, but also statistical, numerical, algebraic properties are described, as well as many new generalizations and applications. Being aware of the growing interest in these techniques, it is a strong belief that this book will aid and stimulate users to apply the new techniques and models correctly to their own practical problems.

Least squares --- Error analysis (Mathematics) --- Academic collection --- 681.3*I54 --- Errors, Theory of --- Instrumental variables (Statistics) --- Mathematical statistics --- Numerical analysis --- Statistics --- Method of least squares --- Squares, Least --- Curve fitting --- Geodesy --- Mathematics --- Probabilities --- Triangulation --- Applications: computer vision; signal processing; text processing; waveform analysis (Pattern recognition) --- Least squares. --- Error analysis (Mathematics). --- 681.3*I54 Applications: computer vision; signal processing; text processing; waveform analysis (Pattern recognition) --- Algebra. --- Matrix theory. --- Statistics . --- Applied mathematics. --- Engineering mathematics. --- Numerical analysis. --- Algorithms. --- Linear and Multilinear Algebras, Matrix Theory. --- Statistics, general. --- Applications of Mathematics. --- Numeric Computing. --- Algorism --- Algebra --- Arithmetic --- Mathematical analysis --- Engineering --- Engineering analysis --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Foundations

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The subject of this book is numerical methods that preserve geometric properties of the flow of a differential equation: symplectic integrators for Hamiltonian systems, symmetric integrators for reversible systems, methods preserving first integrals and numerical methods on manifolds, including Lie group methods and integrators for constrained mechanical systems, and methods for problems with highly oscillatory solutions. A complete theory of symplectic and symmetric Runge-Kutta, composition, splitting, multistep and various specially designed integrators is presented, and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory and related perturbation theories. The book is illustrated by many figures, it treats applications from physics and astronomy and contains many numerical experiments and comparisons of different approaches.

519.62 --- 681.3*G17 --- Numerical methods for solution of ordinary differential equations --- Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- Differential equations --- Hamiltonian systems. --- Numerical integration. --- Numerical solutions. --- 681.3*G17 Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- 519.62 Numerical methods for solution of ordinary differential equations --- Hamiltonian systems --- Numerical integration --- Integration, Numerical --- Mechanical quadrature --- Quadrature, Mechanical --- Definite integrals --- Interpolation --- Numerical analysis --- Hamiltonian dynamical systems --- Systems, Hamiltonian --- Differentiable dynamical systems --- 517.91 Differential equations --- Numerical solutions --- 517.91 --- Dynamique différentiable. --- Systèmes hamiltoniens. --- Differentiable dynamical systems. --- Numerical analysis. --- Mathematical analysis. --- Analysis (Mathematics). --- Mathematical physics. --- Physics. --- Biomathematics. --- Numerical Analysis. --- Analysis. --- Theoretical, Mathematical and Computational Physics. --- Mathematical Methods in Physics. --- Numerical and Computational Physics, Simulation. --- Mathematical and Computational Biology. --- Biology --- Mathematics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Physical mathematics --- Physics --- 517.1 Mathematical analysis --- Mathematical analysis --- Numerical solutions&delete& --- Systèmes hamiltoniens --- Integration numerique --- Analyse numerique --- Equations differentielles