Question

Which option is not correct about direct methods for solving system of linear equations?

(a) In the absence of errors it yields exact solution

(b) Errors arising from round off and truncation may give useless results

(c) Gaussian elimination method is an example

(d) Starts with an initial approximation

I have been asked this question in final exam.

My question is based upon Eigen Value and Time Dependent Problems in chapter Single Variable Problems of Finite Element Method

Answer 1

Right option is (d) Starts with an initial approximation

For explanation I would say: The methods used for solving a system of linear equations are classified as: direct and iterative. Direct methods are those, which, in the absence of round-off and other errors, yield an exact solution in a finite number of elementary arithmetic operations. Indeed the errors arising from round-off and truncation may lead to extremely poor or even useless results. The fundamental method used for direct solutions is Gaussian elimination.