Skip to content
Snippets Groups Projects
Commit 39d16545 authored by Christoph Grüninger's avatar Christoph Grüninger
Browse files

[doc] Fix typos and duplicate words

parent 4bbc8f79
No related branches found
No related tags found
No related merge requests found
Pipeline #
......@@ -83,8 +83,8 @@ there are many libraries available on the internet for doing sparse matrix/vecto
computations. A comprehensive overview is given in \cite{LALinks}.
The
widely availably Basic Linear Algebra Subprograms (BLAS) standard has
been extended to cover als sparse matrices \cite{BLASTForum}. BLAS
widely available Basic Linear Algebra Subprograms (BLAS) standard has
been extended to cover as sparse matrices \cite{BLASTForum}. BLAS
divides the available functions into level 1 (vector operations),
level 2 (vector/matrix operations) and level 3 (matrix/matrix
operations). BLAS for sparse matrices contains only level 1 and 2
......@@ -94,7 +94,7 @@ only a FORTRAN and C interface. As a consequence, the interface is
``coarse grained'', meaning that ``small'' functions such as access to
individual matrix elements is relatively slow.
Generic programming techniqes in C++ offer the possibility to combine
Generic programming techniques in C++ offer the possibility to combine
flexibility and reuse (``efficiency of the programmer'') with fast
execution (``efficieny of the program'') as has been demonstrated with
the Standard Template Library (STL), \cite{Stroustrup} or the Blitz++
......@@ -174,7 +174,7 @@ In mathemetics vectors are elements of a vector space. A vector space
$V(\K)$, defined over a field $\K$, is a set of elements with two
operations: (i) vector space addition $+ : V\times V \to V$ and (ii) scalar
multiplication $* : \K\times V \to V$. These operations obey certain formal
rules, see your favourite textbook on linear algebra,
rules, see your favorite textbook on linear algebra,
e.~g. \cite{LaBook}. In addition a
vector space may be normed, i.~e.~there is a function (obeying certain
rules) $\|.\| : V \to \R$ which measures distance in the vector
......@@ -187,7 +187,7 @@ field, such as $\K=\R$ or $\K=\C$ and take a tensor product:
V = \K^n = \underbrace{\K\times\K\times\ldots\times\K}_{\text{$n$ times}}.
\end{equation*}
$n\in\N$ is called the dimension of the vector space. There are also
infinite-dimensional vector spaceswhich are, however, not of interest
infinite-dimensional vector spaces which are, however, not of interest
in the context here. The idea of tensor products can be generalized.
If we have vector spaces $V_1(\K),\ldots,V_n(\K)$ we can construct a
new vector space by setting
......@@ -628,8 +628,8 @@ The base class
linear maps. The
template parameter \lstinline!X! is the type of the domain and
\lstinline!Y! is the type of the range of the operator. A linear
operator provides the methods \lstinline!apply(const X& x, Y& y)! and
apply \lstinline!applyscaledadd(const X& x, Y& y)! performing the
operator provides the methods \lstinline!apply(const X& x, Y& y)! and
\lstinline!applyscaledadd(const X& x, Y& y)! performing the
operations $y = A(x)$ and $y = y + \alpha A(x)$, respectively.
The subclass
\lstinline!template<class M, class X, class Y> AssembledLinearOperator!
......@@ -726,7 +726,7 @@ providing them with the vector implementation used.
\hline
\textbf{class}&\textbf{implements}\\\hline\hline
\lstinline!LoopSolver!& only apply precoditioner multiple time\\
\lstinline!GradientSolver!& preconditioned radient method\\
\lstinline!GradientSolver!& preconditioned gradient method\\
\lstinline!CGSolver!&preconditioned conjugate gradient method\\
\lstinline!BiCGStab!&preconditioned biconjugate gradient stabilized method\\\hline
\end{tabular}
......@@ -812,10 +812,10 @@ operation ($x = y + \alpha z$) in Tables
\hline
\end{tabular}}}
\end{table}
The code was comiled with the GNU C++
The code was compiled with the GNU C++
compiler version 4.0 with -O3 optimization. In the tables $N$ is the
number of
unknown blocks (equals the number of unknows for the scalar cases in
unknown blocks (equals the number of unknowns for the scalar cases in
Tables \ref{tab:perf_sp}, \ref{tab:perf_daxpy}, \ref{tab:perf_gs}).
The performance for the scalarproduct,
see Table \ref{tab:perf_sp},
......
0% Loading or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment