Exascale platforms expected to be available before the end of
this decade will have 100 million to 1 billion CPU cores.
Due to the large number of components, the probability
that a failure occurs during the execution of an
exascale application is expected to be much higher
than today.

In this talk, I will discuss our recent work on
dependable high performance scientific Computing
via algorithmic fault tolerance.
We have developed highly efficient algorithmic fault tolerance techniques
for selected widely used scientific computing algorithms to
tolerate both soft and hard errors according to
their specific algorithmic characteristics. The algorithms we consider include:
(1). Krylov subspace methods for solving sparse linear systems and
eigenvalue problems
including Conjugate Gradient  method (CG),
Generalized Minimal Residual  method (GMRES) , BiConjugate Gradient
method (BiCG),
BiConjugate Gradient Stabilized   method (Bi-CGSTAB), Arnoldi's method
for  eigenvalue problems,
Lanczos method for symmetric eigenvalue problems, and Lanczos
biorthogonalization for
non-symmetric eigenvalue problems;
(2). Direct methods for solving dense linear systems and eigenvalue problems
including LU, Cholesky, and QR; and
(3). Newton's method for solving systems of non-linear equations.
By leveraging the algorithmic characteristics of the these algorithms,
the proposed techniques sacrifice the generality of Triple Modular Redundancy
technique (for soft errors) and checkpoint/restart technique (for hard errors)
for the sake of higher efficiency.