Sparse Matrix Technology

Chapter 1 covers all fundamental material such as storage schemes, basic definitions and computational techniques needed for sparse matrix technology. It is very convenient to read at least Sections 1 to 9 and Section 12 of Chapter 1 first. The first reading may, however, be superficial. The reader will feel motivated to examine this material in more detail while reading other chapters of the book, where numerous references to sections of Chapter 1 are found. Chapters 2 to 5 deal with the solution of linear algebraic equations. They are not independent. The material in Chapter 2 is rather elementary, but its form of presentation serves as an introduction for Chapters 4 and 5, which contain the important material. Chapter 3 deals with numerical errors in the case where the linear system is sparse, and also serves as an introduction to Chapters 4 and 5. This material is not standard in the literature. Sparse matrix methods and algorithms forthe direct solution of linear equations are presented in Chapters 4 and 5. Chapter 4 deals with symmetric matrices, and Chapter 5 with general matrices. The calculation of eigenvalues and eigenvectors of a sparse matrix, or of a pair of sparse matrices in the case of a generalized eigenvalue problem, is discussed in Chapter 6. Chapter 6 can be read independently, except that some references are made to material in Chapters 1 and 7. Chapters 7, 8 and 9 deal with sparse matrices stored in row-wise format. Algorithms for algebraic operations, triangular factorization and back substitution are explicitly given in Fortran and carefully discussed in Chapter 7. The material in Chapter 1 is a prerequisite, particularlySections 8, 9 and 10 and 12 to 17. In addition, Chapter 2 is a prerequisite for Sections 23 to 28 of Chapter 7. Chapter 8 covers the sparse matrix techniques associated with mesh problems, in particular with the finite element method, and in Chapter 9 we present some general purposeFortran algorithms.