An interval is a natural way of specifying a number that is specified only within certain tolerances. Interval analysis consists of the tools and methods needed to solve linear and nonlinear systems of equations in the presence of data uncertainties. Applications include the sensitivity analysis of solutions of equations depending on parameters, the solution of global nonlinear problems, and the verification of results obtained by finite-precision arithmetic. In this book emphasis is laid on those aspects of the theory which are useful in actual computations. On the other hand, the theory is developed with full mathematical rigour. In order to keep the book self-contained, various results from linear algebra (Perron-Frobenius theory, M- and H- matrices) and analysis (existence of solutions to nonlinear systems) are proved, often from a novel and more general viewpoint. An extensive bibliography is included.
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An interval is a natural way of specifying a number that is specified only within certain tolerances. Interval analysis consists of the tools and methods needed to solve linear and nonlinear systems of equations in the presence of data uncertainties. Applications include the sensitivity analysis of solutions of equations depending on parameters, the solution of global nonlinear problems, and the verification of results obtained by finite-precision arithmetic.
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Interval arithmetic is an elegant tool for practical work with inequalities, approximate numbers, error bounds, and more generally with certain convex and bounded sets. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
linear interval equations, scaled maximum norm, accord algorithm, quadratic approximation property, inverse positive matrices, inclusion isotone, inclusion algebra, sublinear mappings, midpoint inverse, fixed point inverse, mean value form, boundary value form, optimal enclosure, hull inverse, rounded interval arithmetic, subdistributive law, linear enclosures, interval mathematics, interval matrix, outward rounding, interval matrices, arithmetical expressions, interval evaluation, interval extension, sign matrices Key Phrases - Capitalized Phrases (CAPs): (learn more)
Theorem Let, Proposition Let, Proof Let, Corollary Let, Proof Suppose, Lemma Let, Proof Put, Example Let, Proof Define, Proof Expressions, Proof Trivial, Proof Apply Proposition, Proof Write New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Interval arithmetic is an elegant tool for practical work with inequalities, approximate numbers, error bounds, and more generally with certain convex and bounded sets. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
linear interval equations, scaled maximum norm, accord algorithm, quadratic approximation property, inverse positive matrices, inclusion isotone, inclusion algebra, sublinear mappings, midpoint inverse, fixed point inverse, mean value form, boundary value form, optimal enclosure, hull inverse, rounded interval arithmetic, subdistributive law, linear enclosures, interval mathematics, interval matrix, outward rounding, interval matrices, arithmetical expressions, interval evaluation, interval extension, sign matrices Key Phrases - Capitalized Phrases (CAPs): (learn more)
Theorem Let, Proposition Let, Proof Let, Corollary Let, Proof Suppose, Lemma Let, Proof Put, Example Let, Proof Define, Proof Expressions, Proof Trivial, Proof Apply Proposition, Proof Write New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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This book cites 22
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81
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- Introduction to Numerical Analysis by Arnold Neumaier in Back Matter
- Convex Analysis (Princeton Landmarks in Mathematics and Physics) by Ralph Tyrell Rockafellar in Back Matter
- Sensitivity Analysis in Linear Systems by Assem S. Deif in Back Matter
- Numerical Analysis by Frank Owen in Back Matter
- Matrix Iterative Analysis (Springer Series in Computational Mathematics) by Richard S. Varga in Back Matter
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- Scientific Computing, Validated Numerics, Interval Methods (University Series in Mathematics) by Walter Krämer on 8 pages
- Applications of Interval Computations (Applied Optimization) by R. Baker Kearfott on 5 pages
- Advances in Convex Analysis and Global Optimization - Honoring the Memory of C. Caratheodory (1873-1950) (Nonconvex Optimization and Its Applications, ... Optimization and Its Applications (closed)) by Nicolas Hadjisavvas on page 72, page 344, and page 456
- Numerical Software with Result Verification by René Alt on page 189, and page 304
- Complex Interval Arithmetic and Its Applications by Miodrag S. Petkovic on page 135, and Back Matter
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