Texas Instruments TI-89 User Manual - Page 841

LU MATH/Matrix menu LU matrix, lMatName, uMatName, pMatName[, tol] [6,12,18;5,14,31;3,8,18]!m1 ¸ Calculates the Doolittle LU (lower-upper) decomposition of a real or complex matrix. The lower triangular matrix is stored in lMatName, the upper triangular matrix in uMatName, and the permutation matrix (which describes the row swaps done during the calculation) in pMatName. lMatName ù uMatName = pMatName ù matrix 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. 65 12 14 1381 3 8 18 LU m1,lower,upper,perm ¸ Done lower ¸ 15/6 0 1 00 1/2 1/2 1 upper ¸ 60 12 4 1186 0 0 1  perm ¸ 10 0 1 00 0 0 1 • If tol is omitted or not used, the default tolerance is calculated as: 5Eë 14 ù max(dim(matrix)) ù rowNorm(matrix) The LU factorization algorithm uses partial pivoting with row interchanges. [m,n;o,p]!m1 ¸ [ ] m n o p LU m1,lower,upper,perm ¸ lower ¸ Done 1m o 0 1  upper ¸ o 0 p n ì møp o  perm ¸ [ ] 0 1 1 0 mat4data MATH/List menu mat4data mat,data[,row1][,col1][,row2][,col2] Converts a matrix to data. mat4data,m1,d1,1,,,1 ¸ Done Each argument [,row1][,col1][,row2][,col2] can be individually omitted. If row1 is omitted the default is 1. If col1 is omitted the default is 1. If row2 is omitted, the default is "max row." If col2 is omitted, the default is "max column." Appendix A: Functions and Instructions 841