Validated Numerics (eBook)

A Short Introduction to Rigorous Computations

Warwick Tucker (Autor)

eBook Download: EPUB

2011
152 Seiten
Princeton University Press (Verlag)
978-1-4008-3897-4 (ISBN)

A comprehensive, self-contained primer on validated numericsThis textbook provides a comprehensive introduction to the theory and practice of validated numerics, an emerging new field that combines the strengths of scientific computing and pure mathematics. In numerous fields ranging from pharmaceutics and engineering to weather prediction and robotics, fast and precise computations are essential. Based on the theory of set-valued analysis, a new suite of numerical methods is developed, producing efficient and reliable solvers for numerous problems in nonlinear analysis. Validated numerics yields rigorous computations that can find all possible solutions to a problem while taking into account all possible sources of error-fast, and with guaranteed accuracy.Validated Numerics offers a self-contained primer on the subject, guiding readers from the basics to more advanced concepts and techniques. This book is an essential resource for those entering this fast-developing field, and it is also the ideal textbook for graduate students and advanced undergraduates needing an accessible introduction to the subject. Validated Numerics features many examples, exercises, and computer labs using MATLAB/C++, as well as detailed appendixes and an extensive bibliography for further reading.Provides a comprehensive, self-contained introduction to validated numericsRequires no advanced mathematics or programming skillsFeatures many examples, exercises, and computer labsIncludes code snippets that illustrate implementationSuitable as a textbook for graduate students and advanced undergraduates

Warwick Tucker is professor of mathematics and principal investigator for the Computer-Aided Proofs in Analysis (CAPA) Group at Uppsala University in Sweden. He has been honored with several awards, including the European Mathematical Society's Prize for Distinguished Contributions in Mathematics, the R. E. Moore Prize for Applications of Interval Analysis, and the Swedish Mathematical Society's Wallenberg Prize.

Erscheint lt. Verlag	5.7.2011
Zusatzinfo	41 b/w illus. 12 tables.
Verlagsort	Princeton
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften
Schlagworte	absolute value • Accuracy and precision • Addition • Approximation • Approximation error • Arbitrarily large • arithmetic • arithmetic logic unit • Asymptote • automatic differentiation • Bernhard Riemann • Binary number • bisection • Bisection (software engineering) • Brouwer fixed-point theorem • Brute-force search • C++ • Calculation • Cardinality • Cauchy Sequence • Code segment • coefficient • commutative property • Compactification (mathematics) • Compiler • complete metric space • Composition operator • Computation • computer simulation • Condition number • Construction of the real numbers • continuous function • Continuous function (set theory) • Contradiction • convex set • Cubic function • data set • Derivative • Deterministic system (philosophy) • DIAMETER • Differentiable function • differential equation • Dimension • disadvantage • Division by zero • Divisor • Divisor (algebraic geometry) • Double-precision floating-point format • Elementary function • empty set • Equation • error • Error analysis (Mathematics) • existential quantification • Explicit formulae (L-function) • exponential function • exponential growth • exponentiation • fault tolerance • Finite difference • Finite set • Fixed-Point Arithmetic • Fixed point (mathematics) • Fixed-point theorem • floating point • For All Practical Purposes • Formal derivative • formal proof • Franklin D. Roosevelt • Function (mathematics) • fundamental theorem • hausdorff distance • Horner's method • IEEE floating point • implementation • Inequality (mathematics) • inference • Infimum and supremum • Integer • Integral • integral equation • Integrated Development Environment • Integrator • intermediate value theorem • interval arithmetic • Interval class • Interval (mathematics) • inverse trigonometric functions • Iteration • Least significant bit • L'Hôpital's rule • linear equation • Lipschitz continuity • local convergence • logarithm • Logical connective • Machine epsilon • Mathematical Induction • Mathematical Optimization • Mathematical Proof • mathematician • Mathematics • MATLAB • Maxima and minima • Maximal element • mean value theorem • Metric Space • Midpoint method • Monotonic Function • Multiplicative Inverse • natural logarithm • Newton's method • nonlinear system • Normalized number • Normal number • Notation • Numerical analysis • Numerical Integration • Operand • ordinary differential equation • Parameter (computer programming) • Parity (mathematics) • partially ordered set • percentage • Point at infinity • polynomial • Positional notation • Positive real numbers • power series • Power set • Prime number • Public Policy • Public speaking • Pure Mathematics • quadratic function • Quantity • Range (mathematics) • rational function • Rational number • real number • Recursive tree • remainder • Removable singularity • Requirement • result • Riemann sum • Root-finding algorithm • Rounding • round-off error • scientific notation • Series (mathematics) • sibling • Sign bit • Sign (mathematics) • Software • solver • Special case • square root • Statement (computer science) • Sticky bit • Subset • Summation • Taylor series • Theorem • Transfinite number • Transitive relation • Transitivity (grammar) • Trapezoidal rule • Trapezoidal rule (differential equations) • Trigonometric Functions • Twitter • Type variable • Uncountable set • Upper and lower bounds • Variable (computer science) • Variable (mathematics) • Without loss of generality • x86 • Zero of a function
ISBN-10	1-4008-3897-5 / 1400838975
ISBN-13	978-1-4008-3897-4 / 9781400838974

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