MULCHO pt1

What is the definition of an algorithm?

• A set of mathematical equations

• A collection of data

• A directive that indicates all passages needed to solve a specific problem

• A list of programming instructions

What is the machine epsilon in the IEEE 754 standard?

• The largest positive floating-point number

• The largest positive integer

• The smallest positive floating-point number

• The smallest positive integer

What is the relative error bound for the subtraction operation in floating-point arithmetic?

• eps

• 2eps

• eps+1

• 1+eps

What is the main issue with the phenomenon of cancellation in numerical computations?

• It increases the precision of the calculation

• It has no impact on the calculation

• It leads to inaccurate results

• It causes the computer to crash

What is the IEEE 754 representation of the number π in single precision binary floating-point format?

• 0 10000000000 1.1001001000011111101101010100010001000010110100011000

• 1 10000000000 1.1001001000011111101101010100010001000010110100011000

• 1 10000000000 1.0101101111110000101010001011000101000101011101101001

• 0 10000000000 1.0101101111110000101010001011000101000101011101101001

What is the total number of de-normalized numbers in the IEEE 754 double precision binary floating-point system?

• 2^1024

• 2^1023

• 2^53

• 2^52

What is the machine epsilon in the double precision IEEE 754 binary floating-point system?

• 2^-52

• 2^-53

• 2^-1024

• 2^-1023

What is the rounding function in floating-point arithmetic used for?

• To always round down the result

• To minimize the error in the result

• To maximize the error in the result

• To always round up the result

Which method is locally linearly convergent with g(x)=x−f(x)/q?

• Chord Method

• Steffensen Method

• Secant Method

• Newton-Raphson Method

Which method is locally quadratically convergent with g(x)=x−f(x)/f'(x)?

• Steffensen Method

• Secant Method

• Newton-Raphson Method

• Chord Method