• Getting started with Julia
• Linear algebra bootcamp
• Linear systems and the basics of floating-point arithmetic
• QR factorization
• Eigenvalues and eigenvectors
• Eigenvalue computation for sparse matrices
• Classical iterations to solve linear systems
• Krylov methods to solve linear systems
• (A taste of) Direct methods to solve sparse linear systems
• Julia essentials

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 approachable and cartoon characters guide the way. Inside this book, readers will find detailed descriptions of algorithms, implementations in Julia that illustrate concepts and allow readers to explore methods on their own, and illustrations and graphics that emphasize core concepts and demonstrate algorithms. Numerical Linear Algebra with Julia is a textbook for undergraduate and graduate students. It is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory. The book may also serve as a reference for researchers in various fields such as computational engineering, statistics, data-science, and machine learning, who depend on numerical solvers in linear algebra.
(source: Nielsen Book Data)

• Matrix multiplication problems
• Matrix analysis
• General linear systems
• Special linear systems
• Orthogonalization and least squares
• Parallel matrix computations
• The unsymmetric eigenvalue problem
• The symmetric eigenvalue problem
• Lanczos methods
• Iterative methods for linear systems
• Functions of matrices
• Special topics.

The fourth edition of Gene H. Golub and Charles F. Van Loan's classic is an essential reference for computational scientists and engineers in addition to researchers in the numerical linear algebra community. Anyone whose work requires the solution to a matrix problem and an appreciation of its mathematical properties will find this book to be an indispensible tool. This revision is a cover-to-cover expansion and renovation of the third edition. It now includes an introduction to tensor computations and brand new sections on: fast transforms; parallel LU; discrete Poisson solvers; pseudospectra; structured linear equation problems; structured eigenvalue problems; large-scale SVD methods; and, polynomial eigenvalue problems. Matrix Computations is packed with challenging problems, insightful derivations, and pointers to the literature-everything needed to become a matrix-savvy developer of numerical methods and software.
(source: Nielsen Book Data)

• Preface
• 1. Introduction
• 2. Linear equation solving
• 3. Linear least squares problems
• 4. Nonsymmetric Eigenvalue problems
• 5. The symmetric Eigenproblem and singular value decomposition
• 6. Iterative methods for linear systems
• 7. Iterative methods for Eigenvalue problems
• Bibliography
• Index.
• (source: Nielsen Book Data)

Designed for first-year graduate students from a variety of engineering and scientific disciplines, this comprehensive textbook covers the solution of linear systems, least squares problems, eigenvalue problems, and the singular value decomposition. The author, who helped design the widely used LAPACK and ScaLAPACK linear algebra libraries, draws on this experience to present state-of-the-art techniques for these problems, including recommending which algorithms to use in various practical situations. Algorithms are derived in a mathematically illuminating way, including condition numbers and error bounds. Direct and iterative algorithms, suitable for dense and sparse matrices, are discussed. Algorithm design for modern computer architectures, where moving data is often more expensive than arithmetic operations, is discussed in detail, using LAPACK as an illustration. There are many numerical examples throughout the text and in the problems at the ends of chapters, most of which are written in MATLAB and are freely available on the Web.
(source: Nielsen Book Data)

• Preface
• Part I. Fundamental: 1. Matrix-vector multiplication
• 2. Orthogonal vectors and matrices
• 3. Norms
• 4. The singular value decomposition
• 5. More on the SVD
• Part II. QR Factorization and Least Squares: 6. Projectors
• 7. QR factorization
• 8. Gram-Schmidt orthogonalization
• 9. MATLAB
• 10. Householder triangularization
• 11. Least squares problems
• Part III. Conditioning and Stability: 12. Conditioning and condition numbers
• 13. Floating point arithmetic
• 14. Stability
• 15. More on stability
• 16. Stability of householder triangularization
• 17. Stability of back substitution
• 18. Conditioning of least squares problems
• 19. Stability of least squares algorithms
• Part IV. Systems of Equations: 20. Gaussian elimination
• 21. Pivoting
• 22. Stability of Gaussian elimination
• 23. Cholesky factorization
• Part V. Eigenvalues: 24. Eigenvalue problems
• 25. Overview of Eigenvalue algorithms
• 26. Reduction to Hessenberg or tridiagonal form
• 27. Rayleigh quotient, inverse iteration
• 28. QR algorithm without shifts
• 29. QR algorithm with shifts
• 30. Other Eigenvalue algorithms
• 31. Computing the SVD
• Part VI. Iterative Methods: 32. Overview of iterative methods
• 33. The Arnoldi iteration
• 34. How Arnoldi locates Eigenvalues
• 35. GMRES
• 36. The Lanczos iteration
• 37. From Lanczos to Gauss quadrature
• 38. Conjugate gradients
• 39. Biorthogonalization methods
• 40. Preconditioning
• Appendix
• Notes
• Bibliography
• Index.
• (source: Nielsen Book Data)

This is a concise, insightful introduction to the field of numerical linear algebra. The clarity and eloquence of the presentation make it popular with teachers and students alike. The text aims to expand the reader's view of the field and to present standard material in a novel way. All of the most important topics in the field are covered with a fresh perspective, including iterative methods for systems of equations and eigenvalue problems and the underlying principles of conditioning and stability. Presentation is in the form of 40 lectures, which each focus on one or two central ideas. The unity between topics is emphasized throughout, with no risk of getting lost in details and technicalities. The book breaks with tradition by beginning with the QR factorization - an important and fresh idea for students, and the thread that connects most of the algorithms of numerical linear algebra.
(source: Nielsen Book Data)