Least Squares Computations Using Orthogonalization MethodsOrthogonalization, elimination, least squares and correlation. The least suqares problem. Back substitution, forward solution inversion. Classical gram-schmidt vs. modified gram-schmidt. Connection between gram-schmidt, householder and plane rotations. The gram-schmidt algorithm. The inverse matrix. Generalized matrix inversion by gram-schmidt. Singular value decomposition. Advantages and disadvantages of reducing. Programming considerations. |
Contents
Chapter | 1 |
Chapter | 9 |
Back Substitution Forward Solution | 20 |
Copyright | |
24 other sections not shown
Common terms and phrases
1,NPROJ ABAR BETA coefficients bidiagonal matrix CARD Classical Gram-Schmidt coefficient of determination coefficient of nondetermination CONDITION NUMBER DABS data matrix data scaled diagonal elements DSQRT eigenvalue equations F-RATIOS follows FORTRAN GO TO 11 Gram-Schmidt orthogonalization Gram-Schmidt process Householder transformations IFMT IMPLICIT REAL*8 A-H,O-Z inner products iterations JFMT JFORM2 Lanczos Lawson and Hanson LEFT GIVENS length of vector Longley Problem matrix of orthonormal method of Björck Modified Gram-Schmidt multiple coefficient n x n NMGSA normalized data NPROB NPROJ OPTION orthonormal vectors output produced QR Transformation R(IK R(IKK regressand regressor variables residual vector RETURN END SCALED 10 EXP SDBHAT shift parameter shifts in origin side statistics singular value decomposition solution standard deviations STANDARD ERROR Stewart's Sensitivity Index SUBROUTINE SKINNY Table TAMP TEMP TOMP trace and determinant triangular inverse matrix underflow unexplained variance upper triangular inverse upper triangular matrix zero