Description: SuperLU is a general purpose library for the direct solution of large, sparse, nonsymmetric systems of linear equations on high performance machines. The library is written in C and is callable from either C or Fortran. The library routines will perform an LU decomposition with partial pivoting and triangular system solves through forward and back substitution. The LU factorization routines can handle non-square matrices but the triangular solves are performed only for square matrices. The matrix columns may be preordered (before factorization) either through library or user supplied routines. This preordering for sparsity is completely separate from the factorization. Working precision iterative refinement subroutines are provided for improved backward stability. Routines are also provided to equilibrate the system, estimate the condition number, calculate the relative backward error, and estimate error bounds for the refined solutions. -SuperLU is a general purpose library for the direct solution of large, sparse, nonsymmetric systems of linear equations on high performance machines. The library is written in C and is callable from either C or Platform: |
Size: 1955840 |
Author:anfangde |
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Description: Modify the Matlab Gauss Elimination routine given in lectures so that it
(a) performs implicit complete pivoting, and
(b) handles m right hand sides at once by performing an LU decomposition of the matrix A first and
then doing forward substitution and back substitution (hence not modifying the right hand side as the
elimination is perfomed).
Test your program and then run it on the system AX = B-Modify the Matlab Gauss Elimination routine given in lectures so that it (a) performs implicit complete pivoting, and (b) handles m right hand sides at once by performing an LU decomposition of the matrix A first and then doing forward substitution and back substitution ( hence not modifying the right hand side as the elimination is perfomed). Test your program and then run it on the system AX = B Platform: |
Size: 1024 |
Author:liuzhenghao |
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Description: Solving an upper triangular system U x = b by back-substitution
Solving a lower triangular system L x = b by forward-substitution-backward substitution and forward substitution Platform: |
Size: 1024 |
Author:QuanyuZhao |
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Description: Systems of linear equations
Our Matlab function for naive Gaussian
elimination looks like this:
function x = naiv_gauss(A,b)
n = length(b) x = zeros(n,1)
for k=1:n-1 forward elimination
for i=k+1:n
xmult = A(i,k)/A(k,k)
for j=k+1:n
A(i,j) = A(i,j)-xmult*A(k,j)
end
b(i) = b(i)-xmult*b(k)
end
end
back substitution
x(n) = b(n)/A(n,n)
for i=n-1:-1:1
sum = b(i)
for j=i+1:n
sum = sum-A(i,j)*x(j)
end
x(i) = sum/A(i,i)
end-Systems of linear equations
Our Matlab function for naive Gaussian
elimination looks like this:
function x = naiv_gauss(A,b)
n = length(b) x = zeros(n,1)
for k=1:n-1 forward elimination
for i=k+1:n
xmult = A(i,k)/A(k,k)
for j=k+1:n
A(i,j) = A(i,j)-xmult*A(k,j)
end
b(i) = b(i)-xmult*b(k)
end
end
back substitution
x(n) = b(n)/A(n,n)
for i=n-1:-1:1
sum = b(i)
for j=i+1:n
sum = sum-A(i,j)*x(j)
end
x(i) = sum/A(i,i)
end Platform: |
Size: 37888 |
Author:amine |
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Search - forward back substitution