[...] = SBSolve (...)
solve a system of linear equations with a symmetric banded matrix
X=SBSolve(A,B)
[X,R]=SBSolve(A,B)
solves A X = B
A is mxt where t-1 is number of non-zero super diagonals
B is mxn
X is mxn
R is mxt
if A would be ! 11000 ! then A= ! 11 !
! 14300 ! ! 43 !
! 03520 ! ! 52 !
! 00285 ! ! 85 !
! 00059 ! ! 90 !
B is a full matrix
The code is based on a LDL' decomposition (use L=R'), without pivoting.
If A is positive definite, then it reduces to the Cholesky algorithm.
R is an upper right band matrix
The first column of R contains the entries of a diagonal matrix D.
If the first column of R is filled by 1's, then we have R'*D*R = A
