Error Computation in Numerical Analysis

What is round-off error in numerical analysis?

• The exact value obtained in numerical computations

• Theoretical calculations without any errors

• Small discrepancies between the true value and the computed value due to finite precision arithmetic.

• Significant figures in scientific notation

Define truncation error and provide an example.

• Truncation error occurs when a computer program stops running abruptly.

• Truncation error is the difference between the true value and the approximated value.

• An example of truncation error is when a function is integrated using the wrong method.

• An example of truncation error is when the value of pi (π) is approximated as 3.14 instead of its true value of 3.14159...

Calculate the absolute error when the true value is 10 and the approximate value is 8.

• 6

• 5

• 3

• 2

Explain the concept of relative error in numerical analysis.

• Relative error = |True Value - Approximation| / |True Value|

• Relative error = True Value / Approximation

• Relative error = True Value - Approximation

• Relative error = Approximation / True Value

Discuss the impact of truncation error on the accuracy of numerical methods.

• Truncation error has no impact on numerical methods

• Truncation error only affects theoretical calculations

• Truncation error reduces the accuracy of numerical methods by introducing inaccuracies through rounding or cutting off digits during calculations.

• Truncation error improves the accuracy of numerical methods

If the true value of a quantity is 100 and the measured value is 95, calculate the absolute error.

• 3

• 10

• 5

• 2

What is the formula for calculating percentage relative error?

• (|Approximate Value - True Value| / |True Value|) * 100

• True Value / Approximate Value

• True Value - Approximate Value

• Approximate Value / True Value

How does increasing the number of significant digits affect round-off error?

• Increasing the number of significant digits increases round-off error.

• Increasing the number of significant digits only affects precision, not round-off error.

• Increasing the number of significant digits has no effect on round-off error.

• Increasing the number of significant digits decreases round-off error.

Provide an example where round-off error significantly impacts the final result.

• Temperature conversions

• Counting prime numbers

• Financial calculations involving very small or very large numbers

• Simple addition and subtraction

Determine the correct definition of 3 decimal places

• 0.49x10^-3<0.5x10^-3

• 0.55x10^-3<0.5x10^-3

• 0.5x10^-3<0.5x10^-3

• 0.75x10^-3<0.5x10^-3