WZgbsv WZgbsv2 WZgesv WZgesv2 WZgtsv WZgtsv2 WZsysv WZsysv2 WZtrtrs WZtrtrs2

WZgtsv() Function WZgtsv ( N As  Long, Dl As  Variant, D As  Variant, Du As  Variant, B As  Variant, Optional Nrhs As  Long = 1  ) Solution to system of linear equations AX = B for a complex tridiagonal matrix (complex number representation in Excel format) Purpose WZgtsv solves the equation A * X = B where A is an N x N tridiagonal matrix, by Gaussian elimination with partial pivoting. Note that the equation A^T*X = B may be solved by interchanging the order of the arguments Du and Dl. 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] Dl (N-1) Sub-diagonal elements of coefficient matrix A. [in] D (N) Diagonal elements of coefficient matrix A. [in] Du (N-1) Super-diagonal elements of coefficient matrix A. [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) Reference LAPACK Example Solve the system of linear equations Ax = B and estimate the reciprocal of the condition number (RCond) of A, where A is a tridiagonal matrix and ( 0.57-0.91i 0.56+0.92i 0 ) A = ( -1.45-0.81i 1.74-0.93i -0.19-0.16i ) ( 0 0.28+0.09i 0.10+0.15i ) ( -1.0924+1.0032i ) B = ( 1.8436+1.5703i ) ( 0.2057+0.2156i )