Search results
Results from the WOW.Com Content Network
The polyhedral method treats each loop iteration within nested loops as lattice points inside mathematical objects called polyhedra, performs affine transformations or more general non-affine transformations such as tiling on the polytopes, and then converts the transformed polytopes into equivalent, but optimized (depending on targeted ...
In numerical linear algebra, the Arnoldi iteration is an eigenvalue algorithm and an important example of an iterative method.Arnoldi finds an approximation to the eigenvalues and eigenvectors of general (possibly non-Hermitian) matrices by constructing an orthonormal basis of the Krylov subspace, which makes it particularly useful when dealing with large sparse matrices.
This is a list of some of the more commonly known problems that are NP-complete when expressed as decision problems. As there are thousands of such problems known, this list is in no way comprehensive. Many problems of this type can be found in Garey & Johnson (1979).
NumPy (pronounced / ˈ n ʌ m p aɪ / NUM-py) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. [3]
The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries = =. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop:
Hilbert matrix — example of a matrix which is extremely ill-conditioned (and thus difficult to handle) Wilkinson matrix — example of a symmetric tridiagonal matrix with pairs of nearly, but not exactly, equal eigenvalues; Convergent matrix — square matrix whose successive powers approach the zero matrix; Algorithms for matrix multiplication:
1. Open the File Explorer icon on your desktop taskbar. 2. Click the Downloads folder. 3. Double click the Install_AOL_Desktop icon. 4. Click Run. 5. Click Install Now. 6. Restart your computer to finish the installation.
Inputs: A, b, ω Output: φ Choose an initial guess φ to the solution repeat until convergence for i from 1 until n do set σ to 0 for j from 1 until n do if j ≠ i then set σ to σ + a ij φ j end if end (j-loop) set φ i to (1 − ω)φ i + ω(b i − σ) / a ii end (i-loop) check if convergence is reached end (repeat)