Numerical Linear Algebra and Matrix Factorizations
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Beschreibung
After reading this book, students should be able to analyze computational problems in linear algebra such as linear systems, least squares- and eigenvalue problems, and to develop their own algorithms for solving them.
Since these problems can be large and difficult to handle, much can be gained by understanding and taking advantage of special structures. This in turn requires a good grasp of basic numerical linear algebra and matrix factorizations. Factoring a matrix into a product of simpler matrices is a crucial tool in numerical linear algebra, because it allows us to tackle complex problems by solving a sequence of easier ones.The main characteristics of this book are as follows:
It is self-contained, only assuming that readers have completed first-year calculus and an introductory course on linear algebra, and that they have some experience with solving mathematical problems on a computer. The book provides detailed proofs of virtually all results. Further, its respective parts can be used independently, making it suitable for self-study.
The book consists of 15 chapters, divided into five thematically oriented parts. The chapters are designed for a one-week-per-chapter, one-semester course. To facilitate self-study, an introductory chapter includes a brief review of linear algebra.
After reading this book, students should be able to analyze computational problems in linear algebra such as linear systems, least squares- and eigenvalue problems, and to develop their own algorithms for solving them.
Since these problems can be large and difficult to handle, much can be gained by understanding and taking advantage of special structures. This in turn requires a good grasp of basic numerical linear algebra and matrix factorizations. Factoring a matrix into a product of simpler matrices is a crucial tool in numerical linear algebra, because it allows us to tackle complex problems by solving a sequence of easier ones.The main characteristics of this book are as follows:
It is self-contained, only assuming that readers have completed first-year calculus and an introductory course on linear algebra, and that they have some experience with solving mathematical problems on a computer. The book provides detailed proofs of virtually all results.Further, its respective parts can be used independently, making it suitable for self-study.
The book consists of 15 chapters, divided into five thematically oriented parts. The chapters are designed for a one-week-per-chapter, one-semester course. To facilitate self-study, an introductory chapter includes a brief review of linear algebra.
Detailed proofs of practically all results making it suitable for self-study Detailed algorithms in Matlab The book is self-contained, assuming only first year calculus
Autor*in
Tom Lyche
Themen in »Numerical Linear Algebra and Matrix Factorizations«
numerical linear algebra matrix theory MATLAB programming linear systems least squares eigenvalue problems nonlinear equations scientific computing linear algebra numerical stability QR decomposition singular value decomposition tensor products iterative measures
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“It is more suitable for students with a few more advanced courses that include at least some real analysis and introductory numerical analysis.” (Tom Lyche, MAA Reviews, November 7, 2020)
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