ill conditioned system of equations tutorialpoint
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Conditioned
Statistics Definitions >
A mathematical problem or series of equations is ill-conditioned if a small change in the independent variable (input) leads to a large change in the dependent variable (output). This can lead to computational problems. For example, if a system of equations is ill-conditioned, the solution exists, but it if very difficult to find.
Well-conditioning is one of the requirements for well-posed problems. Therefore, an ill-conditioned problem is defined as ill-posed.
Condition Numbers and Ill Conditioning
To make the concept of ill-conditioning concrete we can look at the condition number of a function. A function is simply the relationship between variables. It’s a way to map from one set of data (the input, or independent variable) to another (the output, or dependent variable). For the relationship to be considered a function, every bit of input data gets exactly one output.
Imagine your function graphed, with the independent variable on one axis and the dependent variable on the other. The condition number tells us how steep the slope of a function is at its steepest point.
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Conditioned
Statistics Definitions >
A mathematical problem or series of equations is ill-conditioned if a small change in the independent variable (input) leads to a large change in the dependent variable (output). This can lead to computational problems. For example, if a system of equations is ill-conditioned, the solution exists, but it if very difficult to find.
Well-conditioning is one of the requirements for well-posed problems. Therefore, an ill-conditioned problem is defined as ill-posed.
Condition Numbers and Ill Conditioning
To make the concept of ill-conditioning concrete we can look at the condition number of a function. A function is simply the relationship between variables. It’s a way to map from one set of data (the input, or independent variable) to another (the output, or dependent variable). For the relationship to be considered a function, every bit of input data gets exactly one output.
Imagine your function graphed, with the independent variable on one axis and the dependent variable on the other. The condition number tells us how steep the slope of a function is at its steepest point.
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