A unified treatment is given for iterative algorithms for the solution of the symmetric linear complementarity problem:
 
$$Mx + q \geqslant 0, x \geqslant 0, x^T (Mx + q) = 0$$

 , whereM is a givenn×n symmetric real matrix andq is a givenn×1 vector. A general algorithm is proposed in which relaxation may be performed both before and after projection on the nonnegative orthant. The algorithm includes, as special cases, extensions of the Jacobi, Gauss-Seidel, and nonsymmetric and symmetric successive over-relaxation methods for solving the symmetric linear complementarity problem. It is shown first that any accumulation point of the iterates generated by the general algorithm solves the linear complementarity problem. It is then shown that a class of matrices, for which the existence of an accumulation point that solves the linear complementarity problem is guaranteed, includes symmetric copositive plus matrices which satisfy a qualification of the type:
 
$$Mx + q > 0 for some x in R^n $$

 . Also included are symmetric positive-semidefinite matrices satisfying this qualification, symmetric, strictly copositive matrices, and symmetric positive matrices. Furthermore, whenM is symmetric, copositive plus, and has nonzero principal subdeterminants, it is shown that the entire sequence of iterates converges to a solution of the linear complementarity problem.

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Solution of symmetric linear complementarity problems by iterative methods

A method for calculating spring and damping coefficients for the tilting-pad journal bearing is presented. The analysis includes the effect of pad inertia. Numerical results are given in form of design curves for the centrally pivoted 4-shoe, 5-shoe, 6-shoe, and 12-shoe journal bearing. A comparison with test results is included. This paper deals with the effects of lubricant compressibility on the pressure profile and total load capacity in a partial journal bearing; pivot pressure as a measure of shoe load capacity; shoe friction characteristics; and optimum shoe clearance ratios for various speeds. The parameter λ is used as an indicator of the compressibility effect of gas in the bearing clearance. Contributed by the ASLE Technical Committee on Bearings and Bearing Lubrication and presented at the Annual Meeting of the American Society of Lubrication Engineers held in Chicago, Illinois, May, 1964.

Spring and Damping Coefficients for the Tilting-Pad Journal Bearing

CFD analysis of journal bearing hydrodynamic lubrication by Bingham lubricant

This is the concluding paper in a series. The effect of modifying the assumptions in Parts I and II to include the influence of rupture of the film is discussed in detail. Numerical solutions which account for film rupture are presented for Reynolds' equation in the form of performance curves and tabulated data for centrally-loaded bearings having arcs of 360°, 180°, 120° and 60° for L/D values of ∞ 1, 1/2 and 1/4. The method of obtaining the computer solutions is discussed in the appendix and the results compared with similar work of other investigators. Presented as an American Society of Lubrication Engineers paper at the Lubrication Conference held in Toronto, Canada, October, 1957.

A Solution for the Finite Journal Bearing and its Application to Analysis and Design: III

This Paper presents a survey of important papers pertaining to thermal effects in journal bearings. It includes discussions on theoretical, computation, and experimental works pertaining to heat effects in journal bearings published in various technical journals. Presented at the 4191 Annual Meeting in Toronto, Ontario, Canada May 12–15, 1986

A Review of Thermal Effects in Hydrodynamic Bearings. Part II: Journal Bearings

The effect of pad curvature (fitted pads, clearance pads) on load capacity is analyzed. A potential form of pad instability (“spragging”) is discussed and means of controlling it shown. Contributed to the American Society of Lubrication Engineers by the authors. Manuscript received April 2, 1962.

John Boyd

Papers

A Solution for the Finite Journal Bearing and its Application to Analysis and Design: III

Clearance Considerations in Pivoted Pad Journal Bearings

Applying Bearing Theory to the Analysis and Design of Journal Bearings—II

Self-aligning hydrostatic bearing

The Influence of Fluid Forces on the Sticking and the Lateral Vibration of Pistons