1.7.5. Implementation.

We will use Maple and its ability to control the number of digits in the floating point calculations to illustrate the above ill-conditioned problems.

Consider the 2 by 2 matrix from the trajectory problem.

The Maple procedure Digits is used to control the number of digits.

		> Digits:=10;
		> a:=matrix(2,2,[1,1,1,1.001]);

The Maple procedure cond is used to measure the ill-conditioning.

		> cond(a);
		>4004.001000

The Maple procedure linsolve is used with various numbers of digits.

		> linsolve(a,[1,3]);	
		>[-1999. 2000.]

		> Digits:=3;

			NO SOLUTION....Divide by zero

		> Digits:=4;

		>[-1997. 1998.]

		> Digits:=5;

		>[-1999. 2000.]

Consider the 3 by 3 matrix from the function approximation problem. Assume the function to be approximated satisfies f(1) = 1, f(1.1) = 2 and f(1.11) = 3.

The Maple procedure Digits is used to control the number of digits.

		> Digits:=10;
		a:=matrix(3,3,[1,1,1,1,1.1,1.21,1,1.11,1.2321]);

The Maple procedure cond is used to measure the ill-conditioning.

		> cond(a);
		>14103.66200

The Maple procedure linsolve is used with various numbers of digits.

		> sol:=linsolve(a,[1,2,3]);		
		> sol := [890.9998480 -1708.181530 818.1816817]
		> Digits:=3:

		> sol3:=linsolve(a,[1,2,3]);

		> sol3 := [259. -508. 249.]

		> Digits:=5:

		> sol5 :=linsolve(a,[1,2,3]);

		> sol5 := [897.61 -1720.8 824.19]

		> Digits:=8;

		> sol8:=linsolve(a,[1,2,3]);

		> sol8 := [891.04811 -1708.2737 818.22559]

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