Fundamentals of Matrix Computations

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This modernized edition offers a clear introduction to matrix computations, essential for scientific computing. Retaining the accessible style of its predecessor, it thoroughly details matrix computations and the underlying theory, enriched by the author's insights. The book covers key algorithms in numerical linear algebra, helping readers understand their development and functionality. Notable features include a novel approach to Francis' QR algorithm, classical Gram-Schmidt with reorthogonalization, a revised derivation of the Golub-Reinsch SVD algorithm, and new coverage on solving product eigenvalue problems. It expands on the Jacobi-Davidson method and discusses stopping criteria for iterative methods in solving linear equations. Numerous new and updated exercises, from routine computations to challenging proofs, engage readers in applying concepts. The edition incorporates MATLAB to address real-world problems in areas like electrical circuits and mass-spring systems, with a MATLAB terms index to aid understanding. This book serves as an excellent resource for upper-undergraduate and graduate courses in matrix computations and applied numerical linear algebra, as well as for researchers and practitioners in engineering and computer science needing expertise in matrix computations.