Miroslav Fiedler's Books

This revised and corrected second edition of a classic on special matrices provides researchers in numerical linear algebra and students of general computational mathematics with an essential reference. 1986 edition.

Demonstrates the close relationship between matrix theory and elementary Euclidean geometry, with emphasis on using simple graph-theoretical notions.

Linear programming has attracted the interest of mathematicians since World War II when the first computers were constructed. Early attempts to apply linear programming methods practical problems failed, in part because of the inexactness of the data used to create the models. This book presents a comprehensive treatment of linear optimization with inexact data, summarizing existing results and presenting new ones within a unifying framework.

Large sparse linear systems of equations are ubiquitous in science, engineering and beyond. This open access monograph focuses on factorization algorithms for solving such systems. It presents classical techniques for complete factorizations that are used in sparse direct methods and discusses the computation of approximate direct and inverse factorizations that are key to constructing general-purpose algebraic preconditioners for iterative solvers. A unified framework is used that emphasizes the underlying sparsity structures and highlights the importance of understanding sparse direct methods when developing algebraic preconditioners. Theoretical results are complemented by sparse matrix algorithm outlines. This monograph is aimed at students of applied mathematics and scientific computing, as well as computational scientists and software developers who are interested in understanding the theory and algorithms needed to tackle sparse systems. It is assumed that the reader has completed a basic course in linear algebra and numerical mathematics.

Demonstrates the close relationship between matrix theory and elementary Euclidean geometry, with emphasis on using simple graph-theoretical notions.

Book's by Miroslav Fiedler

Special Matrices and Their Applications in Numerical Mathematics

Special Matrices and Their Applications in Numerical Mathematics

Matrices and Graphs in Geometry

Matrices and Graphs in Geometry

Linear Optimization Problems with Inexact Data

Linear Optimization Problems with Inexact Data

Algorithms for Sparse Linear Systems

Algorithms for Sparse Linear Systems

Matrices and Graphs in Geometry

Matrices and Graphs in Geometry

Special Matrices and Their Applications in Numerical Mathematics

Special Matrices and Their Applications in Numerical Mathematics

Linear Optimization Problems with Inexact Data

Linear Optimization Problems with Inexact Data

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