pracma (version 1.9.9)

trisolve: Tridiagonal Linear System Solver

Description

Solves tridiagonal linear systems A*x=rhs efficiently.

Usage

trisolve(a, b, d, rhs)

Arguments

a

diagonal of the tridiagonal matrix A.

b, d

upper and lower secondary diagonal of A.

rhs

right hand side of the linear system A*x=rhs.

Value

Returns the solution of the tridiagonal linear system as vector.

Details

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.

References

Gander, W. (1992). Computermathematik. Birkhaeuser Verlag, Basel.

See Also

qrSolve

Examples

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