Functions of Matrices: Theory and Computation

Functions of Matrices: Theory and Computation presents mathematical techniques for computing matrix functions, a key topic in applied mathematics and scientific computing. The book combines rigorous mathematical theory with practical computational methods and algorithms. The text covers major approaches including the Jordan canonical form, polynomial interpolation, rational approximation, and iterative methods. Real-world applications span areas such as differential equations, Markov chains, and exponential integrators. Matrix function perturbation theory and numerical stability analysis form core components, with detailed derivations and proofs throughout. MATLAB code examples demonstrate implementations of the discussed algorithms. This work bridges pure mathematical theory and computational practice in matrix analysis, serving both as a reference for researchers and a guide for practitioners implementing matrix function algorithms.

Readers view this book as a detailed technical reference for matrix functions in numerical analysis and computation. Liked: - Clear explanations of advanced mathematical concepts - Comprehensive coverage of both theory and practical implementations - Useful MATLAB code examples throughout - Strong focus on numerical stability and accuracy - Well-organized chapters that build progressively Disliked: - Dense mathematical content requires strong prerequisite knowledge - Limited coverage of some specialized matrix functions - High price point for individual purchase Reviews/Ratings: Goodreads: 4.5/5 (6 ratings) Amazon: 5/5 (3 ratings) One reader on Goodreads noted it "fills an important gap between pure mathematical theory and computational practice." An Amazon reviewer highlighted the "excellent balance between rigor and accessibility." Several mathematicians on MathOverflow recommend it as the definitive reference for matrix function computations, though note it may be challenging for beginners.

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🔢 This groundbreaking work was published in 2008 by SIAM (Society for Industrial and Applied Mathematics) and has become a standard reference for matrix function computations. 📚 Nicholas J. Higham is Royal Society Research Professor and Richardson Professor of Applied Mathematics at The University of Manchester, and has been awarded the Whitehead Prize and the Fröhlich Prize. 💻 The book includes MATLAB implementations of key algorithms, making it both a theoretical resource and practical guide for computational scientists. 🧮 Matrix functions extend the concept of functions of a single variable (like square root or exponential) to matrices, with applications in physics, engineering, and network analysis. 🏆 The text resolves several long-standing problems in matrix function theory, including the precise relationship between matrix functions and matrix polynomials, which had puzzled mathematicians for decades.