One of the benefits of the SVM algorithm with the kernel trick is that the dimension of the problem has little impact on runtime. LIBSVM explicitly supports sparse datasets.
(package e1071) and it throws a lot of warnings
It looks like that package is built onto of LIBSVM. In this case it might be a rare issue where 32 bit precision isn't quite enough - it depends on the warnings you are getting. Switching to a double precision version of LIBSVM as a test and seeing if the results change significantly would be a good sanity check.
the prediction accuracy is very poor
This is hard to tell without your data. It could just be that your data is hard to classify / can't be done well with an SVM, or it could be a symptom of the "warnings" you are getting.
In general, the RBF kernel doesn't provide much benefit in high dimensional spaces. Some results from the LIBSVM group have shown that degree 2 polynomial kernels can often provide some accuracy on sparse datasets. Ultimately, the linear kernel is often good enough for high dimensional problems. For this reason LIBLINEAR also exists, which is explicitly linear SVMs (and logistic regression) only . You probably want to try a linear model on your data as a sanity check as well, you may find logistic regre