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Basic Algebraic and Numerical Concepts
Some Matrix Problems
Storage Schemes and Matrix Multiplication
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ALGOL algorithm analysis approximately backing store backsubstitution Choleski decomposition coefficient matrix column number computation conjugate gradient conjugate gradient method convergence rate corresponding eigenvector decimal diagonal band diagonal elements efficient eigensolution eigenvalue problem error finite difference finite element FORTRAN fully populated Gaussian elimination gives Hence Integer array inverse iteration iteration matrix iterative methods Jacobi iteration linear equations loop main store matrix multiplication modified modulus non-zero elements normally number of multiplications number of non-zero obtained off-diagonal elements operations orthogonal over-relaxation packing scheme performed pivot selection possible power method Premultiplying probability vector procedure reduction step right eigenvectors row and column set of equations shown in Figure simultaneous equations solution solved sparse matrix stochastic matrix storage schemes storage space Sturm sequence submatrix substructure symmetric matrix symmetric positive definite technique total number transformation transpose trial vectors triangular decomposition tridiagonal matrix unsymmetric values variable bandwidth store voltages