restart:with(linalg):

Warning, the assigned name basis now has a global binding

Warning, the protected names norm and trace have been redefined and unprotected

coeffmatrix := proc(L,d) matrix(nops(L),d+1,[seq(seq(L[ii]^jj,jj=0..d),ii=1..nops(L))]): end:deg := 2; Points := [[1,3],[-1,13],[2,1],[-2,33]]; print(cat(seq(`~`,ii=1..50))); A := coeffmatrix([seq(Points[ii][1],ii=1..nops(Points))],deg): b:=matrix(4,1,[seq(Points[ii][2],ii=1..nops(Points))]): A=eval(A), b=eval(b); print(cat(seq(`~`,ii=1..50))); At := transpose(A); M := evalm( evalm(At &* A)^(-1) &* At ): Mb:= evalm( M &* b ): "(At*A)^(-1)*At" = eval(M); "(At*A)^(-1)*At*b" = eval(Mb); print(cat(seq(`~`,ii=1..50))); f := t -> eval(sum(Mb[ii+1,1]*t^ii,ii=0..deg)): evaln(f(t)) = f(t); plot([Points,f(x)],x=-3..3,y=0..40,style=[point,line],colour=black);

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deg := 3; Points := [[1,3],[-1,13],[2,1],[-2,33]]; print(cat(seq(`~`,ii=1..50))); A := coeffmatrix([seq(Points[ii][1],ii=1..nops(Points))],deg): b:=matrix(4,1,[seq(Points[ii][2],ii=1..nops(Points))]): A=eval(A), b=eval(b); print(cat(seq(`~`,ii=1..50))); At := transpose(A); M := evalm( evalm(At &* A)^(-1) &* At ): Mb:= evalm( M &* b ): "(At*A)^(-1)*At" = eval(M); "(At*A)^(-1)*At*b" = eval(Mb); print(cat(seq(`~`,ii=1..50))); f := t -> eval(sum(Mb[ii+1,1]*t^ii,ii=0..deg)): evaln(f(t)) = f(t); plot([Points,f(x)],x=-3..3,y=0..40,style=[point,line],colour=black);

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deg := 2; Points := [[1,4],[-1,5],[2,31],[-2,15]]; print(cat(seq(`~`,ii=1..50))); A := coeffmatrix([seq(Points[ii][1],ii=1..nops(Points))],deg): b:=matrix(4,1,[seq(Points[ii][2],ii=1..nops(Points))]): A=eval(A), b=eval(b); print(cat(seq(`~`,ii=1..50))); At := transpose(A); M := evalm( evalm(At &* A)^(-1) &* At ): Mb:= evalm( M &* b ): "(At*A)^(-1)*At" = eval(M); "(At*A)^(-1)*At*b" = eval(Mb); print(cat(seq(`~`,ii=1..50))); f := t -> eval(sum(Mb[ii+1,1]*t^ii,ii=0..deg)): evaln(f(t)) = f(t); plot([Points,f(x)],x=-3..3,y=-10..40,style=[point,line],colour=black);

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deg := 3; Points := [[1,4],[-1,5],[2,31],[-2,15]]; print(cat(seq(`~`,ii=1..50))); A := coeffmatrix([seq(Points[ii][1],ii=1..nops(Points))],deg): b:=matrix(4,1,[seq(Points[ii][2],ii=1..nops(Points))]): A=eval(A), b=eval(b); print(cat(seq(`~`,ii=1..50))); At := transpose(A); M := evalm( evalm(At &* A)^(-1) &* At ): Mb:= evalm( M &* b ): "(At*A)^(-1)*At" = eval(M); "(At*A)^(-1)*At*b" = eval(Mb); print(cat(seq(`~`,ii=1..50))); f := t -> eval(sum(Mb[ii+1,1]*t^ii,ii=0..deg)): evaln(f(t)) = f(t); plot([Points,f(x)],x=-3..3,y=-10..40,style=[point,line],colour=black);

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