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Questions and Answers
What is the part of logarithm after the decimal point?
What is the part of logarithm after the decimal point?
- Approximation
- Error
- Mantissa (correct)
- Characteristic
The result obtained from a numerical operation is always exact.
The result obtained from a numerical operation is always exact.
False (B)
What is the difference between the true value and the approximation of that value?
What is the difference between the true value and the approximation of that value?
Error
The numerical result obtained from a numerical method is always ______________________.
The numerical result obtained from a numerical method is always ______________________.
Match the following types of errors with their definitions:
Match the following types of errors with their definitions:
What is the ratio of the absolute error to the true value?
What is the ratio of the absolute error to the true value?
Infinite series errors are a type of truncation error.
Infinite series errors are a type of truncation error.
What is the purpose of learning about errors in numerical computation?
What is the purpose of learning about errors in numerical computation?
What is the term for the difference between the true value and the approximation of that value?
What is the term for the difference between the true value and the approximation of that value?
Truncation error occurs when a finite number of terms is used to approximate an infinite series.
Truncation error occurs when a finite number of terms is used to approximate an infinite series.
What is the formula to find the relative error?
What is the formula to find the relative error?
Rounding off a number to a certain number of decimal digits results in a ______________ error.
Rounding off a number to a certain number of decimal digits results in a ______________ error.
Match the following types of errors with their definitions:
Match the following types of errors with their definitions:
If x = 0.0083465, find the relative error if x is rounded off to three decimal digits.
If x = 0.0083465, find the relative error if x is rounded off to three decimal digits.
What is the definition of an error in numerical computation?
What is the definition of an error in numerical computation?
Truncation errors occur when digits are included in the number.
Truncation errors occur when digits are included in the number.
What is the main reason for errors in computation when using normalized floating-point representation?
What is the main reason for errors in computation when using normalized floating-point representation?
The infinite series expansion for sin(x) is terminated after a finite number of terms, resulting in a type of error known as _______________________.
The infinite series expansion for sin(x) is terminated after a finite number of terms, resulting in a type of error known as _______________________.
Match the following types of errors with their definitions:
Match the following types of errors with their definitions:
What is the result of terminating an infinite series expansion, such as sin(x), after a finite number of terms?
What is the result of terminating an infinite series expansion, such as sin(x), after a finite number of terms?
What is the main reason for errors in computation when using infinite series expansions, such as sin(x) or cos(x)?
What is the main reason for errors in computation when using infinite series expansions, such as sin(x) or cos(x)?
In a normalized floating-point representation, the mantissa can accommodate only a limited number of digits, resulting in a type of error known as _______________________.
In a normalized floating-point representation, the mantissa can accommodate only a limited number of digits, resulting in a type of error known as _______________________.
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Study Notes
Errors in Numerical Computation
- Error is defined as the difference between the actual value and the value obtained from the numerical operation.
- Error = actual value – approximate value
- Error = x - xa, where x is the actual value and xa is the approximation.
Errors in Computation
- Computational errors occur due to:
- Normalized floating-point representation
- Truncation of infinite series expansion
- Inefficient algorithm
Truncation and Round-off Errors
- Truncation error occurs when some digits are excluded from the number.
- Truncation error can occur in two situations:
- When numbers are represented in normalized floating-point form.
- The mantissa can accommodate only a few digits.
Truncation Error Examples
- In a hypothetical computer, 0.0356879 would take the form 0.3568E-1 in normalized floating-point representation.
- The mantissa is the part of the logarithm after the decimal point.
Learning Objectives
- Students will learn and understand errors occurring in numerical computation.
- Errors occur due to inefficient algorithms, normalized floating-point representation, and truncation of infinite series expansion.
Absolute and Relative Errors
- Error is the difference between the true value and the approximation of that value.
- Modulus is the positive value of any problem.
Assignment and Activity
- Calculate approximate values, absolute errors, relative errors, and relative percentage errors.
- Find the relative error in computation of x + y.
- Calculate the maximum static error in a thermometer.
- Calculate the maximum error possible in a calculator.
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