Texas Instruments TI-89 User Manual - Page 859

QR MATH/Matrix menu QR matrix, qMatName, rMatName[ , tol] Calculates the Householder QR factorization of a real or complex matrix. The resulting Q and R matrices are stored to the specified MatNames. The Q matrix is unitary. The R matrix is upper triangular. Optionally, any matrix element is treated as zero if its absolute value is less than tol. This tolerance is used only if the matrix has floating-point entries and does not contain any symbolic variables that have not been assigned a value. Otherwise, tol is ignored. • If you use ¥ ¸ or set the mode to Exact/Approx=APPROXIMATE, computations are done using floating-point arithmetic. The floating-point number (9.) in m1 causes results to be calculated in floating-point form. [1,2,3;4,5,6;7,8,9.]!m1 ¸ 14 2 5 3 6   7 8 9. QR m1,qm,rm ¸ Done qm ¸ ..142932...... .904... .301... .ë4.0881...6... .861... ë.301... .408...  rm ¸ 80..124... 9.601... .904... 111..800798...... 0. 0. 0.  • If tol is omitted or not used, the default tolerance is calculated as: 5Eë 14 ù max(dim(matrix)) ù rowNorm(matrix) [m,n;o,p]!m1 ¸ [ ] m n o p The QR factorization is computed numerically using Householder transformations. The symbolic solution is computed using Gram-Schmidt. The columns in qMatName are the orthonormal basis vectors that span the space defined by matrix. QR m1,qm,rm ¸ Done qm ¸ m ë sign(møpì nøo)øo   m2 + o2 m2 + o2   o møsign(møpì nøo)   m2 + o2 m2 + o2 rm ¸  m2 + o2 0 møn+oøp  m2 + o2  |møpì nøo|  m2 + o2 QuadReg MATH/Statistics/Regressions menu QuadReg list1, list2[, [list3] [, list4, list5]] Calculates the quadratic polynomial regression and updates the system statistics variables. All the lists must have equal dimensions except for list5. list1 represents xlist. list2 represents ylist. list3 represents frequency. list4 represents category codes. list5 represents category include list. In function graphing mode: {0,1,2,3,4,5,6,7}! L1 ¸ {4,3,1,1,2,2,3,3}! L2 ¸ QuadReg L1,L2 ¸ ShowStat ¸ {1 2 3 ...} {4 3 1 ...} Done Appendix A: Functions and Instructions 859