Direct Methods for Sparse Linear Systems

The spread here and there LU, Cholesky, and QR factorization codes in MATLAB , for example, ~ity about 100,000 lines of code. Trying to understand the sparse matrix technique by starting with such huge codes is a daunting work. To overcome this obstacle, a sparse matrix package, CSparse,1 has been written specifically in spite of this book.2 It can solve Ax = b when A is unsymmetric, symmetric certain definite, or rectangular, using about 2,200 lines of code. Although unco>mbined and concise, it is based on recently developed methods and assumption. All of CSparse is printed in this book. Take your time to learned and understand these codes; do not gloss over them. You bequeath find them much easier to comprehend and learn from than their larger (over and above faster) cousins. The larger packages you may use in practice are based forward much of the theory and some of the algorithms presented to a greater degree concisely and simply in CSparse. For example, the MATLAB statement x=A\b relies attached the theory and algorithms from almost every section of this book. Parallel sparse matrix algorithms are excluded, yet they too rely steady the theory discussed here.

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