Bøger i Fundamentals of Algorithms serien

Describes state-of-the-art methods for nonlinear equations and shows, via algorithms in pseudocode and Julia with several examples, how to choose an appropriate iterative method for a given problem and write an efficient solver or apply one written by others.

Iterative methods use successive approximations to obtain more accurate solutions. This volume presents historical background, derives complete convergence estimates for all methods, illustrates and provides Matlab codes for all methods, and studies and tests all preconditioners first as stationary iterative solvers.

Discusses the fundamental computational methods used for image reconstruction in computed tomography (CT). Unique in its emphasis on the interplay of modeling, computing, and algorithm development, the book presents underlying mathematical models for motivating and deriving the basic principles of CT reconstruction methods.

The location of an object can often be determined from indirect measurements using a process called estimation. This book explains the mathematical formulation of location-estimation problems and the statistical properties of these mathematical models.

Covers the fundamental ideas related to classical Riemann solutions, including their special structure and the types of waves that arise, as well as the ideas behind fast approximate solvers for the Riemann problem. The emphasis is on the general ideas, but each chapter delves into a particular application.

Shows how modern matrix methods can be applied in data mining and pattern recognition.

Nonlinear matrix equations arise frequently in applied science and engineering. This is the first book to provide a unified treatment of structure-preserving doubling algorithms, which have been recently studied and proven effective for notoriously challenging problems, such as fluid queue theory and vibration analysis for high-speed trains.

Offers an elementary yet comprehensive introduction to the numerical solution of partial differential equations (PDEs). The book provides detailed descriptions of the four major classes of discretization methods for PDEs and runnable MATLAB (R) code for each of the discretization methods and exercises.

Eigenvalue computations are ubiquitous in science and engineering. John Francis's implicitly shifted QR algorithm has been the method of choice for small to medium sized eigenvalue problems since its invention in 1959. This book presents a new view of this classical algorithm.

This brief book on Newton's method is a user-oriented guide to algorithms and implementation. In just over 100 pages, it shows, via algorithms in pseudocode, in MATLAB, and with several examples, how one can choose an appropriate Newton-type method for a given problem, diagnose problems, and write an efficient solver or apply one written by others.

Provides an introduction to the practical treatment of inverse problems by means of numerical methods, with a focus on basic mathematical and computational aspects. To solve inverse problems, the authors demonstrate that insight about them goes hand in hand with algorithms.