Update README to mention new keyword anorm.

README.md

@@ -22,16 +22,42 @@ Pkg.add("Expokit")
 w = expmv!{T}( w::Vector{T}, t::Number, A, v::Vector{T}; kwargs...)
 ```
 The function `expmv!` calculates `w = exp(t*A)*v`, where `A` is a
-matrix or any type that supports `norm`, `size` and `A_mul_B!` and `v` a dense vector by using Krylov subspace projections. The result is
+matrix or any type that supports `size` and `A_mul_B!` and `v` a dense vector by using Krylov subspace projections. The result is
 stored in `w`.
 
 The following keywords are supported
-- `tol`: tolerance to control step size
-- `m`: size of Krylov subspace
-- `norm`: user-supplied norm
+- `tol`: tolerance to control step size (default: `1e-7`)
+- `m`: size of Krylov subspace (default: `min(30,size(A,1))`)
+- `norm`: user-supplied function to calculate vector norm (dafault: `Base.norm`)
+- `anorm`: operator/matrix norm of `A` to estimate first time-step (default: `opnorm(A, Inf)`)
 
 For convenience, the following versions of `expmv` are provided
 ```julia
 v = expmv!{T}( t::Number, A, v::Vector{T}; kwargs...)
 w = expmv{T}( t::Number, A, v::Vector{T}; kwargs...)
 ```
+
+## phimv
+
+```julia
+w = phimv!{T}( w::Vector{T}, t::Number, A, u::Vector{T}, v::Vector{T}; kwargs...)
+```
+The function `phimv!` calculates `w = e^{tA}v + t φ(t A) u` with `φ(z) = (exp(z)-1)/z`, where `A` is a
+matrix or any type that supports `size` and `A_mul_B!`, `u` and `v` are dense vectors by using Krylov subspace projections. The result is stored in `w`. The supported keywords are the same as for `expmv!`.
+
+## chbv
+
+```julia
+chbv!{T}(w::Vector{T}, A, v::Vector{T})
+```
+The function `chbv!` calculates `w = exp(A)*v` using the partial fraction expansion of
+the uniform rational Chebyshev approximation of type (14,14). 
+
+## padm
+
+```julia
+padm(A; p=6)
+```
+The function `padm` calculates the matrix exponential `exp(A)` of `A` using the irreducible 
+(p,p)-degree rational Pade approximation to the exponential function.
+