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****** |
i n p u t ******
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t |
the knot sequence, of length n+kpm
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n |
the dimension of the approximating spline space, i.e., the order
of the linear system to be constructed.
kpm = k+m, the order of the approximating spline
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lenblk |
the maximum length of the array bloks as allowed by the
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dimension statement in | | |
colloc .
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****** |
w o r k a r e a s ******
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work1 |
used in putit, of size (kpm,kpm)
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work2 |
used in putit, of size (kpm,m+1)
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****** |
o u t p u t ******
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bloks |
the coefficient matrix of the linear system, stored in al-
most block diagonal form, of size
kpm*sum(integs(1,i) , i=1,...,nbloks)
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integs |
an integer array, of size (3,nbloks), describing the block
structure.
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integs(1,i) | | |
= number of rows in block i
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integs(2,i) | | |
= number of columns in block i
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integs(3,i) | | |
= number of elimination steps which can be
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carried out in block | | |
i before pivoting might
bring in an equation from the next block.
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nbloks |
number of blocks, equals number of polynomial pieces
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b |
the right side of the linear system, stored corresponding to the
almost block diagonal form, of size sum(integs(1,i) , i=1,...,
nbloks).
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****** |
m e t h o d ******
each breakpoint interval gives rise to a block in the linear system.
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this block is determined by the | | |
k colloc.equations in the interval
with the side conditions (if any) in the interval interspersed ap-
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propriately, and involves the | | |
kpm b-splines having the interval in
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their support. correspondingly, such a block has | | |
nrow = k + isidel
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rows, with | | |
isidel = number of side conditions in this and the prev-
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ious intervals, and | | |
ncol = kpm columns.
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further, because the interior knots have multiplicity | | |
k, we can
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carry out (in slvblk) | | |
k elimination steps in a block before pivot-
ing might involve an equation from the next block. in the last block,
of course, all kpm elimination steps will be carried out (in slvblk).
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see the detailed comments in the solveblok package for further in-
formation about the almost block diagonal form used here.
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