3. the Lagrange basis form of the interpolating polynomial is prohibitively expensive to evaluate. The monomial...

   

Transcribed Image Text:

3. the Lagrange basis form of the interpolating polynomial is prohibitively expensive to evaluate. The monomial basis form (as computed by the method of undetermined coef- ficients) and the divided-difference form both seem to be expensive to evaluate, but they are not. (a) Propose an optimally efficient algorithm for evaluating the monomial basis form of the inter- polating polynomial, and derive the floating point operation complexity of your proposed algo- rithm. Recall a floating point operation, or flop, is a multiplication-addition pair. (b) Repeat (a) for the divided-difference form. 3. the Lagrange basis form of the interpolating polynomial is prohibitively expensive to evaluate. The monomial basis form (as computed by the method of undetermined coef- ficients) and the divided-difference form both seem to be expensive to evaluate, but they are not. (a) Propose an optimally efficient algorithm for evaluating the monomial basis form of the inter- polating polynomial, and derive the floating point operation complexity of your proposed algo- rithm. Recall a floating point operation, or flop, is a multiplication-addition pair. (b) Repeat (a) for the divided-difference form.