Pure and Applied Mathematics: Computational Methods of Linear Algebra

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This popular textbook offers an accessible introduction to solving linear algebraic problems numerically. It provides a solid theoretical foundation while teaching readers to write FORTRAN90 and MATLAB(r) programs. The Second Edition includes new material and pedagogical enhancements based on the author's teaching experience, such as a chapter on modern supercomputing and parallel programming, and fifty percent more examples and exercises to clarify theory and showcase real-world applications. All FORTRAN90 programs are accompanied by MATLAB(r) versions, and an appendix features answers to selected problems. Beginning with fundamental definitions and results from linear algebra, the text explores direct and iterative methods for solving linear systems of equations, linear least-squares problems, linear eigenvalue problems, and linear programming problems. It also covers the fast Fourier transform, a topic often overlooked in similar texts. The final chapter introduces writing computational linear algebra software for today's vector and parallel supercomputers, highlighting double-precision FORTRAN90 subroutines that are documented for clarity, allowing students to follow the program logic easily. MATLAB(r) versions of the codes are provided in an appendix, and machine-readable copies of the codes can be downloaded from the accompanying website. This textbook is ideal for upper-level undergraduates and graduate students, empha