Features of application of algorithm of construction of bidimentional orthonormalizational basis in procedure Gram-Schmidt orthogonalization

Abstract

At the decision of systems of the linear equations a method of QR-decomposition with use Gram-Schmidt orthogonalization there are cases of reception of results of calculations unacceptable on accuracy. For restraint of influence of the found out defect within the framework of procedure Gram-Schmidt orthogonalization we use algorithm of construction bidimentional orthonormalizational basis. In algorithm of construction bidimentional orthonormalizational basis machine-sensitive parameters are applied. The values of parameters established as a result of research provide the control over the order of argument of function specially used in used algorithm, construction of basis with guaranteed accuracy and high accuracy calculated with the help of QR-decomposition to the decision of system of the linear equations. They also block calculation of the decision of system with badly caused matrix and protect the user from reception of doubtful results of calculations. The last is illustrated with the example of system resulted in clause with Gilbert's badly caused matrix.