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Inverse problems arise in practical applications whenever one needs to deduce unknowns from observables. This monograph is a valuable contribution to the highly topical field of computational inverse problems. Both mathematical theory and numerical algorithms for model-based inverse problems are discussed in detail. The mathematical theory focuses on nonsmooth Tikhonov regularization for linear and nonlinear inverse problems. The computational methods include nonsmooth optimization algorithms, direct inversion methods and uncertainty quantification via Bayesian inference. The book offers a com

Inverse problems (Differential equations) --- Numerical analysis --- Numerical solutions. --- Numerical solutions

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This third volume of four finishes the program begun in Volume 1 by describing all the most important techniques, mainly based on Gröbner bases, which allow one to manipulate the roots of the equation rather than just compute them. The book begins with the 'standard' solutions (Gianni-Kalkbrener Theorem, Stetter Algorithm, Cardinal-Mourrain result) and then moves on to more innovative methods (Lazard triangular sets, Rouillier's Rational Univariate Representation, the TERA Kronecker package). The author also looks at classical results, such as Macaulay's Matrix, and provides a historical survey of elimination, from Bézout to Cayley. This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers.

Equations --- Polynomials. --- Iterative methods (Mathematics) --- Numerical solutions.

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517.91 --- Functions, Special --- Numerical solutions --- Asymptotic theory

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This book offers an introduction to cryptology, the science that makes secure communications possible, and addresses its two complementary aspects: cryptography — the art of making secure building blocks — and cryptanalysis — the art of breaking them. The text describes some of the most important systems in detail, including AES, RSA, group-based and lattice-based cryptography, signatures, hash functions, random generation, and more, providing detailed underpinnings for most of them. With regard to cryptanalysis, it presents a number of basic tools such as the differential and linear methods and lattice attacks. This text, based on lecture notes from the author’s many courses on the art of cryptography, consists of two interlinked parts. The first, modern part explains some of the basic systems used today and some attacks on them. However, a text on cryptology would not be complete without describing its rich and fascinating history. As such, the colorfully illustrated historical part interspersed throughout the text highlights selected inventions and episodes, providing a glimpse into the past of cryptology. The first sections of this book can be used as a textbook for an introductory course to computer science or mathematics. Other sections are suitable for advanced undergraduate or graduate courses. Many exercises are included. The emphasis is on providing a (reasonably) complete explanation of the background for some selected systems. < Joachim von zur Gathen has held professorships at the universities of Toronto, Paderborn, and Bonn, each for more than a decade. He is now retired (and active). His numerous visiting professorships were in Australia, Chile, Germany, South Africa, Spain, Switzerland, Uruguay, and USA. He is founder and was editor-in-chief for 25 years of the journal computational complexity, and was on the editorial boards of several other journals. He is listed in various editions of Who's Who in the World.

Numerical solutions of algebraic equations --- Information systems --- Computer. Automation --- cryptografie --- cryptologie

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This book offers readers a primer on the theory and applications of Ordinary Differential Equations. The style used is simple, yet thorough and rigorous. Each chapter ends with a broad set of exercises that range from the routine to the more challenging and thought-provoking. Solutions to selected exercises can be found at the end of the book. The book contains many interesting examples on topics such as electric circuits, the pendulum equation, the logistic equation, the Lotka-Volterra system, the Laplace Transform, etc., which introduce students to a number of interesting aspects of the theory and applications. The work is mainly intended for students of Mathematics, Physics, Engineering, Computer Science and other areas of the natural and social sciences that use ordinary differential equations, and who have a firm grasp of Calculus and a minimal understanding of the basic concepts used in Linear Algebra. It also studies a few more advanced topics, such as Stability Theory and Boundary Value Problems, which may be suitable for more advanced undergraduate or first-year graduate students. The second edition has been revised to correct minor errata, and features a number of carefully selected new exercises, together with more detailed explanations of some of the topics.

Mathematics. --- Ordinary Differential Equations. --- Numerical Analysis. --- Applications of Mathematics. --- Differential Equations. --- Numerical analysis. --- Mathématiques --- Analyse numérique --- Differential equations --- Differential equations, Linear --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Numerical solutions --- Linear differential equations --- 517.91 Differential equations --- Differential equations. --- Applied mathematics. --- Engineering mathematics. --- Mathematical analysis --- Math --- Science --- Differential equations, Linear. --- Numerical solutions. --- Engineering --- Engineering analysis