User:Mikesmith00

$$\Phi_B \lambda = \Psi_B\Psi_B^\dagger g + \Phi_B\Psi_B\gamma = g$$


 * 1) I didn't realize that Wikipedia used Latex formatting for math.
 * 2) I had never heard of Wikiversity before.
 * 3) I found some resources for my college algebra class, such as free books on wikiversity.
 * 4) The radial basis functions section on Wikiversity is completely blank, this could make an interesting topic for me to add.
 * 5) The radial basis section on wikipedia is also very light.

My additions to condition number are in italics. I realize this was a shorter modification than you requested, but I feel that this is a very useful fact to help develop an intuitive feeling for how well a system can be solved, quickly.

Original Introduction to Condition Number In the field of numerical analysis, the condition number of a function with respect to an argument measures the asymptotically worst case of how much the function can change in proportion to small changes in the argument. The "function" is the solution of a problem and the "arguments" are the data in the problem. A problem with a low condition number is said to be well-conditioned, while a problem with a high condition number is said to be ill-conditioned. The condition number is a property of the problem. Paired with the problem are any number of algorithms that can be used to solve the problem, that is, to calculate the solution. Some algorithms have a property called backward stability. In general, a backward stable algorithm can be expected to accurately solve well-conditioned problems. Numerical analysis textbooks give formulas for the condition numbers of problems and identify the backward stable algorithms.

New Introduction to Condition Number In the field of numerical analysis, the condition number of a function with respect to an argument measures the asymptotically worst case of how much the function can change in proportion to small changes in the argument. The "function" is the solution of a problem and the "arguments" are the data in the problem. A problem with a low condition number is said to be well-conditioned, while a problem with a high condition number is said to be ill-conditioned. ''A general rule of thumb is that if the condition number is $$10^k$$, then k digits of accuracy is lost from the solution. ''The condition number is a property of the problem. Paired with the problem are any number of algorithms that can be used to solve the problem, that is, to calculate the solution. Some algorithms have a property called backward stability. In general, a backward stable algorithm can be expected to accurately solve well-conditioned problems. Numerical analysis textbooks give formulas for the condition numbers of problems and identify the backward stable algorithms.