This updated version of "Solving Linear Systems on Vector and Shared Memory Computers" (SIAM, 1990) discusses major elements of the new advanced-architecture computers and recent developments in the solution of systems of linear equations and eigenvalue algorithms for dense and sparse matrices that are designed to exploit these elements. It ......
Numerical Linear Algebra with Julia provides in-depth coverage of fundamental topics in numerical linear algebra, including how to solve dense and sparse linear systems, compute QR factorizations, compute the eigendecomposition of a matrix, and solve linear systems using iterative methods such as conjugate gradient. The style is friendly and ......
This textbook introduces key numerical algorithms used for problems arising in three core areas of scientific computing: calculus, differential equations, and linear algebra. Theoretical results supporting the derivation and error analysis of algorithms are given rigorous justification in the text and exercises, and a wide variety of detailed ......
This self-contained textbook presents matrix analysis in the context of numerical computation with numerical conditioning of problems and numerical stability of algorithms at the forefront. Using a unique combination of numerical insight and mathematical rigour, it advances readers' understanding of two phenomena: sensitivity of linear systems and ......
Dynamical systems arise in all fields of applied mathematics. The author focuses on the description of numerical methods for the detection, computation and continuation of equilibria and bifurcation points of equilibria of dynamical systems. This subfield has the particular attraction of having links with the geometric theory of differential ......
Conservation laws are the mathematical expression of the principles of conservation and provide effective and accurate predictive models of our physical world. Although intense research activity during the last decades has led to substantial advances in the development of powerful computational methods for conservation laws, their solution remains ......
Methods for the numerical simulation of dynamic mathematical models have been the focus of intensive research for well over 60 years, and the demand for better and more efficient methods has grown as the range of applications has increased. Mathematical models involving evolutionary partial differential equations (PDEs) as well as ordinary ......
This revised edition discusses numerical methods for computing the eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting ......
The method of least squares was discovered by Gauss in 1795. It has since become the principal tool for reducing the influence of errors when fitting models to given observations. Today, applications of least squares arise in a great number of scientific areas, such as statistics, geodetics, signal processing, and control. In the last 20 years ......
