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The book is designed for researchers, students and practitioners interested in using fast and efficient iterative methods to approximate solutions of nonlinear equations. The following four major problems are addressed. Problem 1: Show that the iterates are well defined. Problem 2: concerns the convergence of the sequences generated by a process and the question of whether the limit points are, in fact solutions of the equation. Problem 3: concerns the economy of the entire operations. Problem 4: concerns with how to best choose a method, algorithm or software program to solve a specific type

Funktionalanalysis. --- Iteration. --- Iterative methods (Mathematics). --- Lehrbuch. --- Numerische Mathematik. --- Iterative methods (Mathematics) --- Engineering & Applied Sciences --- Applied Mathematics --- Numerical analysis. --- Mathematical analysis --- Iteration (Mathematics) --- Numerical analysis

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"Deep Learning for Medical Applications with Unique Data informs readers about the most recent deep learning-based medical applications in which only unique data gathered in real cases are used. The book provides examples of how deep learning can be used in different problem areas and frameworks in both clinical and research settings, including medical image analysis, medical image registration, time series analysis, medical data synthesis, drug discovery, and pre-processing operations. The volume discusses not only positive findings, but also negative ones obtained by deep learning techniques, including the use of newly developed deep learning techniques rarely reported in the existing literature."--

Deep learning (Machine learning) --- Learning, Deep (Machine learning) --- Iterative methods (Mathematics) --- Machine learning --- Artificial intelligence --- Deep Learning --- Medical applications

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This text is a self-contained Second Edition, providing an introductory account of the main topics in numerical analysis. The book emphasizes both the theorems which show the underlying rigorous mathematics and the algorithms which define precisely how to program the numerical methods. Both theoretical and practical examples are included.* a unique blend of theory and applications* two brand new chapters on eigenvalues and splines* inclusion of formal algorithms* numerous fully worked examples* a large number of problems, many with solutions

Differential equations -- Numerical solutions. --- Numerical analysis. --- Numerical analysis -- Data processing. --- Applied Mathematics --- Engineering & Applied Sciences --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Iterative methods (Mathematics) --- Analyse numérique --- Itération (mathématiques) --- Intégration numérique.

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The solutions of systems of linear and nonlinear equations occurs in many situations and is therefore a question of major interest. Advances in computer technology has made it now possible to consider systems exceeding several hundred thousands of equations. However, there is a crucial need for more efficient algorithms.

The main focus of this book (except the last chapter, which is devoted to systems of nonlinear equations) is the consideration of solving the problem of the linear equation Ax = b by an iterative method. Iterative methods for the solution of this question are described which are based on projections. Recently, such methods have received much attention from researchers in numerical linear algebra and have been applied to a wide range of problems.

The book is intended for students and researchers in numerical analysis and for practitioners and engineers who require the most recent methods for solving their particular problem.

Lineaire vergelijkingen. --- Projectiemethoden (wiskunde) --- Equations, Simultaneous --- Iterative methods (Mathematics) --- Itération (Mathématiques) --- Numerical solutions. --- -Iterative methods (Mathematics) --- #TELE:SISTA --- 519.6 --- 681.3*G13 --- Iteration (Mathematics) --- Numerical analysis --- Simultaneous equations --- Numerical solutions --- Computational mathematics. Numerical analysis. Computer programming --- Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 681.3*G13 Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Equations, Simultaneous - Numerical solutions.

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Explainable Deep Learning AI: Methods and Challenges presents the latest works of leading researchers in the XAI area, offering an overview of the XAI area, along with several novel technical methods and applications that address explainability challenges for deep learning AI systems. The book overviews XAI and then covers a number of specific technical works and approaches for deep learning, ranging from general XAI methods to specific XAI applications, and finally, with user-oriented evaluation approaches. It also explores the main categories of explainable AI - deep learning, which become the necessary condition in various applications of artificial intelligence. The groups of methods such as back-propagation and perturbation-based methods are explained, and the application to various kinds of data classification are presented.

Artificial intelligence --- Deep learning (Machine learning) --- Design and construction. --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Learning, Deep (Machine learning) --- Iterative methods (Mathematics) --- Machine learning --- Machine learning. --- Explanation-based learning.