In numerical analysis, the condition number of a function measures how much the output value of the function can change for a small change in the input...

In mathematics, the convergence condition by Courant–Friedrichs–Lewy (CFL) is a necessary condition for convergence while solving certain partial differential...

programming Medical condition, as a synonym for disease Medical state or condition, a patient's clinical status in a hospital Condition number, a measure of...

ill-conditioned even when the problem is not. For the problem of solving the linear equation Av = b where A is invertible, the matrix condition number κ(A−1...

linear algebra by the condition number, which (roughly) measures how close a system of equations is to being dependent (a condition number of infinity is a...

most O(ε log n), where ε is the machine precision (assuming a fixed condition number, as discussed below). In comparison, the naive technique of accumulating...

a condition number for any matrix: cond ( A ) = ‖ A ‖ ‖ A + ‖ . {\displaystyle {\mbox{cond}}(A)=\|A\|\left\|A^{+}\right\|.} A large condition number implies...

\Sigma |x_{i}|/|\Sigma x_{i}|} is the condition number of the summation problem. Essentially, the condition number represents the intrinsic sensitivity...

backward error are related by the condition number: the forward error is at most as big in magnitude as the condition number multiplied by the magnitude of...

conditioning, air conditioning in a vehicle Ice storage air conditioning, air conditioning using ice storage Solar air conditioning, air conditioning...

popular alternatives. The number of gradient descent iterations is commonly proportional to the spectral condition number κ ( A ) {\displaystyle \kappa...

solving methods. Preconditioning is typically related to reducing a condition number of the problem. The preconditioned problem is then usually solved by...

significantly, making it unreliable as a stopping condition. This poor convergence is not explained by the condition number alone (e.g., κ 2 ( A ) = 10 6 {\displaystyle...

initial data multiplied by the condition number of A. For instance, if b is known to six decimal places and the condition number of A is 1000 then we can only...

kissing number for n-dimensional spheres in (n + 1)-dimensional Euclidean space? More unsolved problems in mathematics In geometry, the kissing number of a...

Air conditioning, often abbreviated as A/C (US) or air con (UK), is the process of removing heat from an enclosed space to achieve a more comfortable interior...

A chronic condition (also known as chronic disease or chronic illness) is a health condition or disease that is persistent or otherwise long-lasting in...

search algorithm. Provided the linear system is sparse and has a low condition number κ {\displaystyle \kappa } , and that the user is interested in the...

The Kutta condition is a principle in steady-flow fluid dynamics, especially aerodynamics, that is applicable to solid bodies with sharp corners, such...

adding positive elements to the diagonals, thereby decreasing its condition number. Analogous to the ordinary least squares estimator, the simple ridge...

In other words, a problem is ill-conditioned if its conditions number is "much larger" than 1. The condition number is introduced as a measure of the...

and if A is not too ill-conditioned (and the iteration and the rate of convergence are determined by the condition number of A). More formally, assuming...

coordinate system, number 0 denotes the zeroth boundary condition (boundedness) at the center of the cylinder (r = 0), and number 3 denotes the type 3...

system is "singular" precisely if its condition number is infinite, and it is "ill-conditioned" if the condition number is very large. Information data loss:...

of great benefit for numeric stability. One implication is that the condition number is 1 (which is the minimum), so errors are not magnified when multiplying...

the computed inverse to small changes in the original matrix. The condition number is computed by finding the maximum singular value divided by the minimum...

the condition number of the interpolation matrix will diverge to infinity as ε → 0 {\displaystyle \varepsilon \to 0} leading to ill-conditioning of the...

In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value,: pp. 160  is a value of an evolving variable...

domain of f. More generally, the condition can be formulated for functions between any two metric spaces. The number α {\displaystyle \alpha } is called...

Operant conditioning, also called instrumental conditioning, is a learning process in which voluntary behaviors are modified by association with the addition...