Aug 18, 1989 - Nielson's -splines [6] and in a bivariate analogue of tensor product interpolation. In [8], the authors have shown that for any weight function which .... A natural question arising at this point concerns the choice of weight function.
!!
!
" # $ %
& ' ( ) " # " # "#
*
"#
"# + ,
, "#
! " # $ %% & ' ' ( # %% & ' ' )* % !! %&" $' '$#'$%( ($ "#$
-./
-.-
"!#
0+
",#
"!# 0
" # 0+
Ê
+*
" #
1 1 0 2 1 3 " #"# 0+ "# " # 4 "# " # 5 2 + !" # ! Æ ) 4 0+ " #"# + , + + * % " # + " # + * 6 " # + "# '
" 7 # 8& 1 "9# " # + " # + 9 , ! ' 0+ "!# 0 "9# & "/# " # + Æ "# Æ "# Æ : Æ 7 0+ "# ; &
" # + Æ
½
-.
" # + " # " #"# " #"# + " # + " # + * ! ? " # @ 9 1 ' " $ 0+ " + * ' " # + * 5 "# + " ' " # + " + * ) & + 4 %
$ " # " # "# , "# # + , 9 "# "# "# + * "# " # 0 , $ "# $
½ !
"
% * % ' # "$ $# "$ $#
"#
+
½ ½
" $"## ""#
" $"## "#
#
"##
"#
"#
-.A
+!+# , -&+./#& 0 +&
½
%
%
>
" $"## %
½ ½
" $"## "# "
"##
" "## "# " $#
" "## "# " "## "# "$ $# "$ $# * $ "$ $# " # " # "$ $# > " # " # "$ $# " # " $# + * "$ $# + " " $ # " $ ## + " # 4 " $ $ # " $ $# + "$ $# " # * ' "# , " $ $# ", #" $ $# * ") " #
, # ' ' "# 0+ ", ,9# "# "#
3 !
"!# ! (
"& # + &"# "# + &"# & "
# ' $ " $#"# + " $ # " $ $# " # *
½
½
½
-..
' " # % &
1 + '
! ' 9 ' 1 ( "#$%$# ' " # + " # + * ' ' * ! ' ' , 1 "# 0+ '"# "# ,
#
: "# + * '"# + * " "## + , " #
-.B
+!+# , -&+./#& 0 +&
$ 3 ( '
Ê
"# "# ("# +
·½
·½
+
"# "# ("# '"#("#
+ '"#("#
·½
·½
'"#("#
+ '" #(" # '" #(" # '"# ("# + * " # + " # + * '" # + '" # + * ( "# + ( " # ( " # + * ) 1 &'() , ' 9 /
; '"# - , 9 $ % &
"#
·½
·½
·½
-B*
< ' - & * , ,* & , / < - < ,= : "# % , ,9 , /A
, ,. , /, '
,+. & 1 %
+!+# , -&+./#& 0 +&
-B,
,+. & * 1 %1 %1
,+. & ( 1 % 2 1
-B9
,+. & " # 2
3
,+. & ) # 1 4 %1 %1 2 % 2 2
+!+# , -&+./#& 0 +&
-B/
C88C858 05 1 11 6( # ,1 '! #. 789 '.
769 * *" '! #! 789 6 6 5 !
%% : 4 %%1 4: 4 + !: 4 0 %%1 4: : '1 4 ; ; 8 .! 1
7 & 11 ,
1 9 0 2 1== 0 = ! 5 ! 7*9 7*9 8>) 88