A computational error occurs when the output of an algorithm or a computation deviates from the expected or correct result due to various reasons such as hardware faults, software bugs, or numerical inaccuracies. Understanding the causes and methods of mitigating these errors is critical to ensure the reliability and accuracy of computational processes across different applications.
Floating point arithmetic is a method of representing real numbers in a way that can support a wide range of values by using a fixed number of digits. It is essential in computing for handling very large or very small numbers, but it introduces rounding errors and precision limitations due to its finite representation of infinite real numbers.
Validation and verification are critical processes in ensuring that a product meets its intended use and specifications. While verification checks if the product was built correctly according to design, validation ensures that the right product was built to fulfill user needs and requirements.
Machine precision is like the smallest toy block you can use to build something without it falling apart. It tells us how tiny a number can be before a computer thinks it's zero and stops caring about it.