Are the following true or false? GIVE YOUR REASONING. (a) When applied to a syst

Question

Are the following true or false? GIVE YOUR REASONING. (a) When applied to a system with N variables, Gaussian elimination with scaled partial pivoting requires O(N2 ) additional floating point operations over Gaussian elimination with partial pivoting.

(b) Choleski’s method can solve Ax = b for any diagonal, invertible matrix A.

(c) Rounding the number 0.145 to two decimal places gives 0.14.

(d) Suppose the data {(xi , f(xi))} n i lie on a straight line. Then we know the Lagrange interpolating polynomial for the function f is a straight line.

(e) The l norm and the l2 norm of a diagonal matrix are equal.

Explanation / Answer

(a) When applied to a system with N variables, Gaussian elimination with scaled partial pivoting requires O(N2 ) additional floating point operations over Gaussian elimination with partial pivoting.

TRUE. The Gaussian elimination with scaled partial pivoting requires more operations.

(b) Choleski’s method can solve Ax = b for any diagonal, invertible matrix A.

TRUE: The determinant of a diagonoal invertible matrix exists and hence the Choleski's method can solve Ax = b.

(c) Rounding the number 0.145 to two decimal places gives 0.14.

FALSE: rounding the number gives -0.15.

(d) Suppose the data {(xi , f(xi))} n i lie on a straight line. Then we know the Lagrange interpolating polynomial for the function f is a straight line.

TRUE. Because for a straight line function only the data would like on straight line.

(e) The l norm and the l2 norm of a diagonal matrix are equal.

TRUE: Diagonal matrix don't need the difference.

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