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Many improved algorithms have been suggested since 1974. [1] Fast NNLS (FNNLS) is an optimized version of the Lawson–Hanson algorithm. [ 2 ] Other algorithms include variants of Landweber 's gradient descent method, [ 10 ] coordinate-wise optimization based on the quadratic programming problem above [ 7 ] , and an active set method called TNT-NN.
The standard convergence condition (for any iterative method) is when the spectral radius of the iteration matrix is less than 1: ρ ( D − 1 ( L + U ) ) < 1. {\displaystyle \rho (D^{-1}(L+U))<1.} A sufficient (but not necessary) condition for the method to converge is that the matrix A is strictly or irreducibly diagonally dominant .
In early 2005, NumPy developer Travis Oliphant wanted to unify the community around a single array package and ported Numarray's features to Numeric, releasing the result as NumPy 1.0 in 2006. [9] This new project was part of SciPy. To avoid installing the large SciPy package just to get an array object, this new package was separated and ...
In mathematics and logic, the term "uniqueness" refers to the property of being the one and only object satisfying a certain condition. [1] This sort of quantification is known as uniqueness quantification or unique existential quantification, and is often denoted with the symbols "∃!" [2] or "∃ =1". For example, the formal statement
The golden-section search is a technique for finding an extremum (minimum or maximum) of a function inside a specified interval. For a strictly unimodal function with an extremum inside the interval, it will find that extremum, while for an interval containing multiple extrema (possibly including the interval boundaries), it will converge to one of them.
algorithm Gauss–Seidel method is inputs: A, b output: φ Choose an initial guess φ to the solution repeat until convergence for i from 1 until n do σ ← 0 for j from 1 until n do if j ≠ i then σ ← σ + a ij φ j end if end (j-loop) φ i ← (b i − σ) / a ii end (i-loop) check if convergence is reached end (repeat)
Tolerance analysis is the general term for activities related to the study of accumulated variation in mechanical parts and assemblies. Its methods may be used on other types of systems subject to accumulated variation, such as mechanical and electrical systems.
Thus a tolerance is like a congruence, except that the assumption of transitivity is dropped. [1] On a set, an algebraic structure with empty family of operations, tolerance relations are simply reflexive symmetric relations. A set that possesses a tolerance relation can be described as a tolerance space. [2]