discipline of numerical linear algebra, a matrix splitting is an expression which represents a given matrix as a sum or difference of matrices. Many iterative...

iterative method is determined by the matrix splitting A = M − N {\displaystyle A=M-N} and the iteration matrix C = I − M − 1 A {\displaystyle C=I-M^{-1}A}...

matrix T converges to the zero matrix. A regular splitting of a non-singular matrix A results in a convergent matrix T. A semi-convergent splitting of...

algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions;...

approximation to the solution operator as well. List of operator splitting topics Matrix splitting Strang, Gilbert. On the construction and comparison of difference...

equations GRADELA — simple gradient elasticity model Matrix splitting — general method of splitting a matrix operator into a sum or difference of matrices Paul...

columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number...

Luo, he resolved a long-standing open question on the convergence of matrix splitting algorithms for linear complementarity problems and affine variational...

of failure include delamination, intralaminar matrix cracking, longitudinal matrix splitting, fiber/matrix debonding, and fiber fracture. The cause of fiber...

large systems. General iterative methods can be developed using a matrix splitting. Root-finding algorithms are used to solve nonlinear equations (they...

Gauss-Seidel is "column-oriented." See, for example, this paper.) Matrix splitting Richardson iteration Sauer, Timothy (2006). Numerical Analysis (2nd ed...

In linear algebra, the trace of a square matrix A, denoted tr(A), is the sum of the elements on its main diagonal, a 11 + a 22 + ⋯ + a n n {\displaystyle...

of redirect targets Matrix decomposition – Representation of a matrix as a product Matrix splitting – Representation of a matrix as a sum NAG Numerical...

according to the first principal coordinate of the pairwise dissimilarity matrix), splitting the sorted list into equal sized groups (called relative frequency...

calculated and k is the last calculated result. This is in essence a Matrix splitting method, similar to the Jacobi method, applied to the large, sparse...

algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi. Let...

splitting is a quantum system with two states whose unperturbed Hamiltonian is a diagonal operator: Ĥ0 = E0 I, where I is the 2 × 2 identity matrix....

a matrix of the multiplied corresponding elements. This operation can be thought as a "naive matrix multiplication" and is different from the matrix product...

plate, the nail matrix and the nail bed below it, and the grooves surrounding it. The nail matrix is the active tissue (or germinal matrix) that generates...

but fail for the others. Jacobi method Gaussian Belief Propagation Matrix splitting Young, David M. (May 1, 1950), Iterative methods for solving partial...

Because matrix multiplication is such a central operation in many numerical algorithms, much work has been invested in making matrix multiplication algorithms...

value decomposition — unitary matrix times diagonal matrix times unitary matrix Matrix splitting — expressing a given matrix as a sum or difference of matrices...

done in the radix-2 FFT and the Fast Walsh–Hadamard transform. Splitting a known matrix into the Kronecker product of two smaller matrices is known as...

M2 with M1 ≤ A ≤ M2. Every regular splitting of A is convergent. Stability There exists a positive diagonal matrix D such that AD + DAT is positive definite...

In linear algebra, the Frobenius companion matrix of the monic polynomial p ( x ) = c 0 + c 1 x + ⋯ + c n − 1 x n − 1 + x n {\displaystyle p(x)=c_{0}+c_{1}x+\cdots...

(right/left). Each Pauli matrix is Hermitian, and together with the identity matrix I (sometimes considered as the zeroth Pauli matrix σ0 ), the Pauli matrices...

of the positively charged nucleus. This phenomenon is detectable as a splitting of spectral lines, which can be thought of as a Zeeman effect product...

Zero-field splitting (ZFS) describes various interactions of the energy levels of a molecule or ion resulting from the presence of more than one unpaired...

of the matrix product, which uses row-wise splitting of matrices with a given quantity of rows, was proposed by V. Slyusar in 1996. This matrix operation...

call a field E a splitting field for A over K if A⊗E is isomorphic to a matrix ring over E. Every finite dimensional CSA has a splitting field: indeed,...