Intro Flashcards
What is Numerical Computation?
It is the computational analysis of the problem solving processes with the aim of developing an efficient solution algorithm that can be implemented in a computing machine.
What are the differences between Numerical Analysis and Numerical Computation?
Numerical Analysis (NA) and Numerical Computation (NC)
- Infinity exists as an instance to reckon or count in NA but in NC infinity is outside its scope (ambit). Machines deal with finite.
- NA states and transitions exist in constants and variables | NC states and transitions exist in operations and operands.
- In NA the instance of zero exists to be counted/ reckoned and manipulated, but in NC zero is number neutral.
- For NA an implementation tool (e.g computing) is not in view | for NC an implementation tool is in view
- NA process is expressed in language of algebra | NC process is expressed in the language of algorithms
What is a computing machine?
A computing machine is a device which accepts data and instructions, processes the data, and generates an output that is in line with the instructions given.
What is accuracy?
Suppose X is the exact in mind (expected number), and X’ was the result of calculation, then the accuracy of X’ is the measure of its proximity or closeness to the value X
What are the limitations of signed magnitude method of storing numbers?
- The existence of two expressions for zero ( +0 = 00000000; -0 = 10000000)
- The need to dedicate a bit to represent a signed number.
What is the advantage of One’s Complement?
It eliminates the need for reserving a bit for the number’s sign (sign of the number is the number itself).
What is the limitation of One’s Complement?
It has two expressions for zero: +0 = 00000000 and -0 = 11111111
What is Absolute Error?
/ A - A’ /
Where A = desired value,
A’ = result/measured value
What is Relative error?
Absolute error ÷ desired value (or real number)
What is percentage error?
Relative error × 100
What is machine epsilon?
Smallest number a machine can record.
What is machine gamma?
Largest number a machine can reckon.
What is error?
Suppose a number A is the expected value, and A’ is the result of calculations, the error is the difference between A and A’.
A = A’ + e, where e is the error.
What is truth?
Truth is an instance in the context-sensitive universe of human mental conception and is unique to the individual; there is no prescription for truth.
What is Precision?
Precision is the number of digits reckoned in the data representation for a fraction.
What is mistake?
Mistake is the unwitting execution of an incorrect process.
What are the sources of errors?
- Abstraction error
- Inherent error
- Logic precision error
What is abstraction error?
Is error from defective way of thinking about the problem solving process. It has more stages: Theoretical, Assumption, Formulation, Blunder or Mistake.
What is Inherent Error?
Arises from limitations in language in expressing the problem-solving process.
What are the types of errors?
- Abstraction error
- Inherent Error
- Logical Precision Error
What is Logical Precision Error?
Errors that arise from processing floating point numbers on a digital computer. It results from limitations in data storage and data manipulation.
What is the relationship between machine epsilon and machine gamma?
e = Γ-1 ÷ 2.0
Where e = machine epsilon
Γ = machine gamma
What happens when a machine encounters a number smaller than its epsilon value?
- Underflow flag is raised.
- Zero is reckoned.
What happens when a machine encounters a number larger than its gamma value?
- Overflow flag is raised.
- A ‘NaN’ (Not a Number) is reckoned or stored.
