Numerical Methods and Their Applications to Linear Algebra

This edited book, "Numerical Methods and their applications to Linear Algebra", is a collection of contemporary open access articles that highlight new numerical methods and computational techniques for solving of linear algebra problems. Comprised of 11 chapters, this book consists of five major section: Section 1, Chapters 1 to 3, focuses on the matrix and eigenvalue decompositions. It begins by presenting an algorithm for QR decomposition based on the Gram-Schmidt orthogonalization followed by several iterative methods for computing the singular-value decomposition of a large sparse matrix and eigenvalue decomposition of para-Hermitian matrices. Section 2, Chapters 4 and 5, focuses on the matrix perturbation analysis, the nonlinear matrix differences, the inverse eigenvalue problem and the construction of a tridiagonal matrix with specified multiple eigenvalues. Section 3, Chapters 6 to 7, focus on the stability analysis and numerical methods for solving differential algebraic equations. Section 4, Chapters 8 to 9, presents several examples of numerical algebra techniques applied to engineering, scientific and real-world problems. Several iterative methods based on Newton iteration, Poisson integration model, an iterative Krylov subspace solver are also featured in this section. Section 5, Chapters 10 to 11, introduces the reader to the development of a variable-metric adaptive projected subgradient method, new techniques for linear arithmetic based on the linear cube transformation. The intended audience of this edited book will mainly consist of graduate or advanced undergraduate students in engineering, science, and mathematics. The contents of this volume will also be of particular interest to researching academics in engineering and science whom to update their knowledge of modern numerical linear algebra methodologies. Book jacket.