enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Tridiagonal matrix algorithm - Wikipedia

    en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm

    Indeed, multiplying each equation of the second auxiliary system by , adding with the corresponding equation of the first auxiliary system and using the representation = +, we immediately see that equations number through of the original system are satisfied; it only remains to satisfy equation number .

  3. Gaussian elimination - Wikipedia

    en.wikipedia.org/wiki/Gaussian_elimination

    For example, to solve a system of n equations for n unknowns by performing row operations on the matrix until it is in echelon form, and then solving for each unknown in reverse order, requires n(n + 1)/2 divisions, (2n 3 + 3n 2 − 5n)/6 multiplications, and (2n 3 + 3n 2 − 5n)/6 subtractions, [10] for a total of approximately 2n 3 /3 operations.

  4. Tridiagonal matrix - Wikipedia

    en.wikipedia.org/wiki/Tridiagonal_matrix

    Although a general tridiagonal matrix is not necessarily symmetric or Hermitian, many of those that arise when solving linear algebra problems have one of these properties. Furthermore, if a real tridiagonal matrix A satisfies a k , k +1 a k +1, k > 0 for all k , so that the signs of its entries are symmetric, then it is similar to a Hermitian ...

  5. LU decomposition - Wikipedia

    en.wikipedia.org/wiki/LU_decomposition

    The cost of solving a system of linear equations is approximately floating-point operations if the matrix has size . This makes it twice as fast as algorithms based on QR decomposition , which costs about 4 3 n 3 {\textstyle {\frac {4}{3}}n^{3}} floating-point operations when Householder reflections are used.

  6. System of linear equations - Wikipedia

    en.wikipedia.org/wiki/System_of_linear_equations

    The simplest method for solving a system of linear equations is to repeatedly eliminate variables. This method can be described as follows: In the first equation, solve for one of the variables in terms of the others. Substitute this expression into the remaining equations. This yields a system of equations with one fewer equation and unknown.

  7. Cramer's rule - Wikipedia

    en.wikipedia.org/wiki/Cramer's_rule

    In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. It expresses the solution in terms of the determinants of the (square) coefficient matrix and of matrices obtained from it by replacing one column by the ...

  8. Lis (linear algebra library) - Wikipedia

    en.wikipedia.org/wiki/Lis_(linear_algebra_library)

    Lis (Library of Iterative Solvers for linear systems; pronounced lis]) is a scalable parallel software library to solve discretized linear equations and eigenvalue problems that mainly arise from the numerical solution of partial differential equations using iterative methods.

  9. Matrix multiplication - Wikipedia

    en.wikipedia.org/wiki/Matrix_multiplication

    Matrix multiplication is thus a basic tool of linear algebra, and as such has numerous applications in many areas of mathematics, as well as in applied mathematics, statistics, physics, economics, and engineering. [3] [4] Computing matrix products is a central operation in all computational applications of linear algebra.