Matrix Stretching for Linear Equations

Stretching is a new sparse matrix method that makes matrices sparser by making them larger. Stretching has implications for computational complexity theory and applications in scientific and parallel computing. It changes matrix sparsity patterns to render linear equations more easily solved by parallel and sparse techniques. Some stretchings increase matrix condition numbers only moderately, and thus solve linear equations stably. For example, these stretchings solve arrow equations with accuracy and expense preferable to other solution methods. for introducing me to the need and practice of solving two-point boundary value problems. Their use of the analytic transformations in Section 7 prompted this work.