Matrices and Linear Algebra with SCILAB
... write the summation symbol, Σ, with its associated indices, if he used the convention that, whenever two indices were repeated in an expression, the summation over all possible values of the repeating index was implicitly expressed. Thus, the equation for the generic term of a matrix multiplication, ...
... write the summation symbol, Σ, with its associated indices, if he used the convention that, whenever two indices were repeated in an expression, the summation over all possible values of the repeating index was implicitly expressed. Thus, the equation for the generic term of a matrix multiplication, ...
Generalized Eigenvectors
... coefficient matrix. Now we turn to situations where some eigenvalues do not have as many linearly independent eigenvectors as their multiplicities. In such cases we shall use generalized eigenvectors as a substitute for regular eigenvectors. They can be used to express A as A = TJT-1 where J, called ...
... coefficient matrix. Now we turn to situations where some eigenvalues do not have as many linearly independent eigenvectors as their multiplicities. In such cases we shall use generalized eigenvectors as a substitute for regular eigenvectors. They can be used to express A as A = TJT-1 where J, called ...
Ferran O ón Santacana
... Dealing efficiently with Linear Algebra Operations on parallel computers: ScaLAPACK ScaLAPACK: Scalable Linear Algebra Package [15,16] Is a subset of LAPACK routines redesigned for distributed memory MIMD parallel computers written in FORTRAN77 It is portable on any computer that supports MPI ...
... Dealing efficiently with Linear Algebra Operations on parallel computers: ScaLAPACK ScaLAPACK: Scalable Linear Algebra Package [15,16] Is a subset of LAPACK routines redesigned for distributed memory MIMD parallel computers written in FORTRAN77 It is portable on any computer that supports MPI ...
Iterative Methods for Systems of Equations
... The simplest iterative method is called Jacobi iteration and the basic idea is to use the A = L + D + U partitioning of A to write AX = B in the form DX = −(L + U )X + B. We use this equation as the motivation to define the iterative process DX (k+1) = −(L + U )X (k) + B which gives X (k+1) as long ...
... The simplest iterative method is called Jacobi iteration and the basic idea is to use the A = L + D + U partitioning of A to write AX = B in the form DX = −(L + U )X + B. We use this equation as the motivation to define the iterative process DX (k+1) = −(L + U )X (k) + B which gives X (k+1) as long ...
Spectrum of certain tridiagonal matrices when their dimension goes
... sequence {x1 (λ), x2 (λ), . . . , xN +1 (λ)}. It is easily verified that the only way n(λ), as a function of λ, can change its value is when xN +1 (λ) goes through zero, and each time this happens, n(λ) changes by 1. Thus, the number of times n(λ) changes is a lower bound for the number of zeros of x ...
... sequence {x1 (λ), x2 (λ), . . . , xN +1 (λ)}. It is easily verified that the only way n(λ), as a function of λ, can change its value is when xN +1 (λ) goes through zero, and each time this happens, n(λ) changes by 1. Thus, the number of times n(λ) changes is a lower bound for the number of zeros of x ...
