• Major optimization of dense numerical linear algebra.

• New optimized sparse numerical linear algebra.

• Support for optimized arbitrary-precision linear algebra.

• Generalized eigenvalues and singular value decomposition.

• LinearSolveFunction for repeated linear-system solving.

• norms for vectors and matrices.

• Built-in MatrixRank for exact and approximate matrices.

• Support for large-scale linear programming, with interior point methods.

• New methods and array variable support in FindRoot and FindMinimum.

• FindFit for full nonlinear curve fitting.

• Constrained global optimization with NMinimize.

• Support for -dimensional PDEs in NDSolve.

• Support for differential-algebraic equations in NDSolve.

• Support for vector and array-valued functions in NDSolve.

• Highly extensive collection of automatically accessible algorithms in NDSolve.

• Finer precision and accuracy control for arbitrary-precision numbers.

• Higher-efficiency big number arithmetic, including processor-specific optimization.

• Enhanced algorithms for number-theoretical operations including GCD and FactorInteger.

• Direct support for high-performance basic statistics functions.