That's why, sort of ... Classical mechanics derived from self-evident axioms

That's why, sort of ....; Classical Mechanics derived from Self-evident Axioms

Classical point-mechanics is derived from three principles —called axioms— that are based on observations of simple kinematical phenomena. Predefined concepts of ‘force’ and ‘mass’ are not required. The concept ’mass’ and corresponding concepts of momentum and energy follow from the first and second axiom. Together with the third axiom, a basic...

On the Convergence Behavior of IDR(s) and Related Methods

An explanation is given of the convergence behavior of IDR(s) methods. The convergence mechanism of these algorithms has two components. The first consists of damping properties of certain factors in the residual polynomials, which becomes less important for large values of s. The second component depends on the behavior of Lanczos polynomials...

An elegant IDR(s) variant that efficiently exploits bi-orthogonality properties

The IDR(s) method that is proposed in [18] is a very efficient limited memory method for solving large nonsymmetric systems of linear equations. IDR(s) is based on the induced dimension reduction theorem, that provides a way to construct subsequent residuals that lie in a sequence of shrinking subspaces. The IDR(s) algorithm that is given in [18...

On the statistical properties of solutions of completely random linear systems

In this report the probability distributions of x and kxk are derived, where x is the solution of a finite square, completely random linear system, i.e. a system Ax = b, of which all entries are stochastically independent, and standard Gaussian distributed stochastic variables. The question on the statistical behaviour of kxk came up in [5], the...

On the convergence behaviour of IDR(s)

An explanation is given of the convergence behaviour of the IDR(s) methods. The convergence of the IDR(s) algorithms has two components. The first consists of damping properties of certain factors in the residual polynomials, which becomes less important for large values of s. The second component depends on the behaviour of quasi-Lanczos...

An elegant IDR(s) variant that efficiently exploits bi-orthogonality properties

Bi-CGSTAB as an induced dimension reduction method

Nonnegative matrix factorization of a correlation matrix

IDR(s): A family of simple and fast algorithms for solving large nonsymmetric linear systems

Some properties of the generalized eigenvalue problem Mx=λ(Γ - cI)x, where M is the infinitesimal generator of a Markov process, and Γ is a real diagonal matrix

Errors in cubic spline interpolation