◆ WZptsv()

Function WZptsv	(	N As	Long,
		D As	Variant,
		E As	Variant,
		B As	Variant,
		Optional Nrhs As	Long = `1`
	)

Solution to system of linear equations AX = B for a Hermitian positive definite tridiagonal matrix (complex number representation in Excel format)

Purpose: WZptsv computes the solution to a complex system of linear equations
A * X = B,

where A is an N x N Hermitian positive definite tridiagonal matrix, and X and B are N x Nrhs matrices.

A is factored as A = L*D*L^H, and the factored form of A is then used to solve the system of equations.

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 leading minor of order i of A is not positive definite, so the factorization could not be completed, and the solution has not been computed.

Parameters

[in]	N	Number of linear equations, i.e., order of the matrix A. (N >= 1)
[in]	D	(N) Diagonal elements of the N x N coefficient matrix A.
[in]	E	(N-1) Subdiagonal elements of the N x N 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 an Hermitian positive definite tridiagonal matrix and
( 2.88 0.29-0.44i 0 )

A = ( 0.29+0.44i 0.62 -0.01-0.02i )

( 0 -0.01+0.02i 0.46 )

( 1.6236-0.7300i )

B = ( 0.1581+0.1537i )

( 0.1132-0.2290i )

WZptsv