Tridiagonal Linear System Solver
Solves tridiagonal linear systems A*x=rhs efficiently.
trisolve(a, b, d, rhs)
a |
diagonal of the tridiagonal matrix |
b, d |
upper and lower secondary diagonal of |
rhs |
right hand side of the linear system |
Solves tridiagonal linear systems A*x=rhs by applying Givens
transformations.
By only storing the three diagonals, trisolve has memory requirements
of 3*n instead of n^2 and
is faster than the standard solve function for larger matrices.
Returns the solution of the tridiagonal linear system as vector.
Has applications for spline approximations and for solving boundary value problems (ordinary differential equations).
Gander, W. (1992). Computermathematik. Birkhaeuser Verlag, Basel.
set.seed(8237) a <- rep(1, 100) e <- runif(99); f <- rnorm(99) x <- rep(seq(0.1, 0.9, by = 0.2), times = 20) A <- diag(100) + Diag(e, 1) + Diag(f, -1) rhs <- A %*% x s <- trisolve(a, e, f, rhs) s[1:10] #=> 0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9 s[91:100] #=> 0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9
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