C Library Functions - bchslv (3)

from * a practical guide to splines * by c. de boor

solves the linear system
c*x = b of order n r o w for x

provided
w contains the cholesky factorization for the banded (sym-

metric) positive definite matrix
c as constructed in the subroutine

b c h f a c
(quo vide).

******

i n p u t ******

nrow.....is the order of the matrix

c .

nbands.....indicates the bandwidth of

c .

w.....contains the cholesky factorization for

c , as output from

subroutine bchfac
	(quo vide).

b.....the vector of length

n r o w containing the right side.

******

o u t p u t ******

b.....the vector of length
	n r o w containing the solution.

******

m e t h o d ******

with the factorization
	c = ldl-transpose available, where l is
unit lower triangular and
	d is diagonal, the triangular system
*ly = b**	is solved for y (forward substitution), y is stored in b,
the vector
	d*(-1)y is computed and stored in b, then the triang-
ular system
	l-transposex = d(-1)y is solved for x (backsubstit- ution).

Nemo Release 3.1

bchslv (3)

June 29, 2025

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