Preconditioned Conjugate Gradient
نویسندگان
چکیده
.. ................................................................................................................... ix Chapter 1. Introduction ..................................................................................................1 Chapter 2. Background ..................................................................................................6 2.1. Matrix Computation ............................................................................................ 6 2.1.1. Storage Format for Vector and Matrix ................................................................... 6 2.1.1. Matrix/Vector Add/Subtract/Multiplication ........................................................... 7 2.1.1. Matrix Solver – Direct Method .............................................................................. 8 2.1.2. Matrix Solver – Multiplication of Inverse Matrix ................................................ 10 2.2. Sparse Matrix .................................................................................................... 10 2.2.1. Coordinate Format (COO) .................................................................................... 11 2.2.2. Compressed Sparse Row/Column Format (CSR / CSC) ...................................... 12 2.2.3. Ellpack-Itpack Format (ELL) ............................................................................... 12 2.2.4. Diagonal Storage Format (DIA) ........................................................................... 13 2.2.5. Hybrid Formats ..................................................................................................... 13 2.3. Iterative Methods .............................................................................................. 14 2.3.1. Conjugate Gradient Method ................................................................................. 15 2.3.2. Preconditioner ...................................................................................................... 15 2.3.2.1. Jacobi, SGS, SOR and SSOR Preconditioners ............................................................ 17
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