Class of Incomplete Orthogonal Factorization Methods. 1. Methods and Theories

摘要

The authors study the solution of large sparse nonsingular and unsymmetric211u001esystems of linear equations. The authors present a class of incomplete orthogonal 211u001efactorization methods based on Givens rotations. These methods include: 211u001eIncomplete Givens Orthogonalization (IGO-method) and Generalized Incomplete 211u001eGivens Orthogonalization (GIGO-method), which drop entries from the incomplete 211u001eorthogonal and upper triangular factors by position; Threshold Incomplete Givens 211u001eOrthogonalization (TIGO(tau)-method), which drops entries dynamically by their 211u001emagnetudes; and Generalized Threshold Incomplete Givens Orthogonalization 211u001e(GTIGO(tau, rho)-method), which drops entries dynamically by both their 211u001emagnitudes and positions. Theoretical analyses show that these methods can 211u001eproduce a nonsingular sparse nonsingular incomplete orthogonal factor for a 211u001egeneral nonsingular matrix.