Solve almost block-diagonal linear system
x = slvblk(blokmat,b)
x = slvblk(blockmat,b,w)
x = slvblk(blokmat,b) returns the solution
(if any) of the linear system Ax = b, with the matrix
A stored in blokmat in the spline almost
block-diagonal form. At present, only the command spcol provides
such a description, of the matrix whose typical entry is the value of some
derivative (including the 0th derivative, i.e., the value) of a B-spline at some
site. If the linear system is overdetermined (i.e., has more equations than unknowns
but is of full rank), then the least-squares solution is returned.
The right side b may contain several columns, and is expected
to contain as many rows as there are rows in the matrix described by
blokmat.
x = slvblk(blockmat,b,w) returns the
vector x that minimizes the weighted sum
Σjw(j)((Ax
– b)(j))2.
sp=spmak(knots,slvblk(spcol(knots,k,x,1),y.')) provides in
sp the B-form of the spline s of order k
with knot sequence knots that matches the given data
(x,y), i.e., for which s(x) equals
y.
The command bkbrk is used to obtain the essential parts of the
coefficient matrix described by blokmat (in one of two available
forms).
A QR factorization is made of each diagonal block, after it was augmented by the equations not dealt with when factoring the preceding block. The resulting factorization is then used to solve the linear system by back substitution.