WZgbsv WZgbsv2 WZgesv WZgesv2 WZgtsv WZgtsv2 WZsysv WZsysv2 WZtrtrs WZtrtrs2

WZgbsv() Function WZgbsv ( N As  Long, Kl As  Long, Ku As  Long, Ab As  Variant, B As  Variant, Optional Nrhs As  Long = 1  ) Solution to system of linear equations AX = B for a complex band matrix (complex number representation in Excel format) Purpose Zgbsv computes the solution to a complex system of linear equations A * X = B where A is a band matrix of order N with Kl sub-diagonals and Ku super-diagonals, and X and B are N x Nrhs matrices. The LU decomposition with partial pivoting and row interchanges is used to factor A as A = L * U where L is a product of permutation and unit lower triangular matrices with Kl sub-diagonals, and U is upper triangular with Kl+Ku super-diagonals. The factored form of A is then used to solve the system of equations A * X = B. To represent complex numbers in Excel cells, complex number format in Excel (e.g. 2.5+1i) is used. Worksheet function Complex can be used to input complex numbers into cells. Returns N+2 x Nrhs Column 1 Column 2 . . . Column Nrhs Rows 1 to N Solution matrix X Row N+1 Reciprocal condition number 0 . . . 0 Row N+2 Return code 0 . . . 0 Return code. = 0: Successful exit. = i > 0: The i-th diagonal element of the factor is zero. (Matrix A is singular) Parameters [in] N Number of linear equations, i.e., order of the matrix A. (N >= 1) [in] Kl The number of subdiagonals within the band of A. (Kl >= 0) [in] Ku The number of superdiagonals within the band of A. (Ku >= 0) [in] Ab (Kl+1+Ku x N) N x N coefficient matrix A. (Band matrix form. See below for details) [in] B (N x Nrhs) N x Nrhs right hand side matrix B. [in] Nrhs (Optional) Number of columns of right hand side matrix B. (Nrhs >= 1) (default = 1) Further Details The band matrix form is illustrated by the following example, when N = 6, Kl = 2, Ku = 1: * a12 a23 a34 a45 a56 a11 a22 a33 a44 a55 a66 a21 a32 a43 a54 a65 * a31 a42 a53 a64 * * Cells marked with * are not used by the routine. Reference LAPACK Example Solve the system of linear equations Ax = B and estimate the reciprocal of the condition number (RCond) of A, where ( 0.81+0.37i 0.20-0.11i 0 ) A = ( 0.64+0.51i -0.80-0.92i -0.93-0.32i ) ( 0 0.71+0.59i -0.29+0.86i ) ( -0.0484+0.2644i ) B = ( -0.2644-1.0228i ) ( -0.5299+1.5025i )