**CURRICULUM VITA**

Steven Arthur Pruess

**Current professional address:**
Mathematical and Computer Sciences Department

Colorado School of Mines

Golden, Colorado, 80401-1887

303-273-3869

**E-mail:** spruess@mines.edu

**Home address:**

1133 N Desert Deer Pass

Green Valley, Arizona 85614-5530

**Education:**
B.S. in Mathematics, Iowa State University, 1966.

M.S. in Computer Science, Purdue University, 1968.

Ph.D. in Computer Science, Purdue University, 1970.

**Professional Employment:**

Dept. of Mathematical and Computer Sciences, Colorado School of Mines, 1998 - (Emeritus)

Dept. of Mathematical and Computer Sciences, Colorado School of Mines, 1986 - 1998

Dept. of Mathematics, University of New Mexico, 1970 - 1986

**Visiting Positions:**

1980 - 1981 Dept. of Computer Science, University of British Columbia, Vancouver.

1982 (summer) Institute for Advanced Study, Australian National University, Canberra.

1985 (June) Math & CS Division, Argonne National Laboratory.

1987 (May-June) Dept. of Mathematics, National Autonomous University of Mexico.

**Professional societies:** Society of Industrial and Applied Mathematics

**Teaching (at Purdue University):**

CS 414 - Introduction to Numerical Analysis

**Teaching (at the University of New Mexico):**

CS 150 - Introduction to Computer Programming

Math 155 - Programming in FORTRAN

Math 162 - Calculus I

Math 163 - Calculus II

Math 180 - Calculus I for Business and Social Sciences

Math 264 - Calculus III

Math 265 - Vector Calculus

Math 312 - Engineering Math I

Math 314 - Linear Algebra with Applications

Math 315 - Engineering Math II

Math 316 - Ordinary Differential Equations

Math 375 - Numerical Methods

Math 464 - Applied Matrix Theory

Math 475 - Numerical Analysis I

Math 476 - Numerical Analysis II

Math 557 - Topics in Numerical Analysis - Spline Applications

Math 557 - Topics in Numerical Analysis - PDE

Math 672 - Advanced Numerical Analysis - Eigenvalues

**Teaching (at the Los Alamos Graduate Center of the University of New Mexico):**

Math 505 - Numerical Linear Algebra

Math 582 - Applied Functional Analysis

**Teaching (at the University of British Columbia):**

CpSci 350 - Programming of Numerical Algorithms

CpSci 402 - Numerical Linear Algebra

**Teaching (at the National Autonomous University of Mexico):**

Cursillo on "Splines and Their Applications"

**Teaching (at the Colorado School of Mines):**
CS 260 - Fortran Programming

CS 290 - Programming Concepts and Data Structures

CS 341 - Machine Organization / Assembler Language

CS 441 - Introduction to Computer Graphics

Math 131 - Calculus I

Math 315 - Differential Equations

Math 332 - Linear Algebra

Math 337 - Advanced Engineering Mathematics (Rocky Flats)

Math/CS 407 - Introduction to Numerical Methods

Math/CS 408 - Numerical Analysis

Math 500 - Linear Vector Spaces

Math/CS 550 - Numerical Methods for PDEs

Math/CS 551 - Numerical Linear Algebra

**Thesis and Dissertation Students:**

Master of Science (Colorado School of Mines)

J. Kevin Samuel, A Method for Estimating the Hausdorff Dimension of a
Planar Line Pattern, August 1988.

Eric Thaler, Numerical Solutions to the Shallow Water Equations as
Applied to a Local Meteorological Forecast Problem, December 1989.

H. Jin, A Stable High Order Interpolation Scheme for Superconvergent
Data, October 1993.

Z. Hu, Parallel Implementation of the Software Package SLEDGE on a
Cluster of Workstations, May 1997.

W. Wang, A Database Application for Use in Reservoir Fluids, March 1998.

T. Minke, MPIPOV: Distributed Ray Tracing on a Network of Workstations,
June 1998.

E. Duckworth, Sturm-Liouville Solver for the Worldwide Web, June 1998.

L. Huang, Automated Software testing Project in GES32 Development,
November 1998.

A. Safray, Parametric Curves and Surfaces with Stepwise Curvature and
Their Use for CAD/CAM Functions, June 1999.

N. Supakata, A Study of the Component Object Model Implementations of
a Numerical Heat Flow Model, September 1999.

Ph.D. (University of New Mexico)

Mahmoud Sarhan, Numerical Methods for Multi-Point Boundary Value
Problems, May 1977.

James C. Ferguson, Shape Preserving Parametric Cubic Curve
Interpolation, June 1984.

Jin Hau Su, The Properties of 1D and 2D Approximation by a Class of
Piecewise Cubic Splines, June 1986.

Humberto Madrid, Analysis of Fast Rational QR Algorithms for Symmetric
Tridiagonal Matrices, July 1986.

Ph.D. (Colorado School of Mines)

H. Jin, Uniformly Superconvergent Interpolation Schemes for Solutions of
First Order Systems of Two Point Boundary Value Problems, November 1995.

M. Rymes, Minimum-curvature Cp surface generation using tin-based
piecewise bipolynomials, December 1996.

**Publications:**

- Titchmarsh-Weyl theory for tridiagonal Jacobi matrices and computation of their spectral functions, with Charles Fulton and David Pearson, in Advances in Mathematical Problems in Engineering, Aerospace and Sciences, ed. by S. Sivasundaram, Cambridge Scientific, 2008, Chapter 5, pp. 167-174.
- Efficient calculation of spectral density functions for specific classes of singular Sturm-Liouville problems, with Charles Fulton and David Pearson, J. Comp. Appl. Math., 212 (2008), pp. 150-178.
- New characterizations of spectral density functions for singular Sturm-Liouville problems, with Charles Fulton and David Pearson, J. Comp. Appl. Math., 212 (2008), pp. 194-213.
- Computing the spectral function for singular Sturm-Liouville problems, with Charles Fulton and David Pearson, J. Comp. Appl. Math., 176 (2005), pp. 131-162.
- A rate-based model for the design of gas absorbers for the removal of CO2 and H2S using aqueous solutions of MEA and DEA, with Nadhir Al-Baghli, Victor Yesavage, and Sami Selim, Fluid Phase Equilibria, 185 (2001), pp. 31-43.
- Qualitatively correct Sturm-Liouville eigenfunction approximation, Appl. Num. Math., 34 (2000), pp. 127-141.
- Chiral baryon in the coherent pair approximation, with T. Aly and J. McNeil, Phys. Rev. D 60, 114022 (1999).
- The computation of spectral density functions for singular Sturm-Liouville problems involving (simple) continuous spectra, with Charles Fulton, ACM Trans. on Math. Software, 24 (1998), pp. 107-129.
- Stable uniformly superconvergent interpolants for two-point boundary value problems, with H. Jin, SIAM J. Numer. Anal., 35(1998), pp. 363-375.
- Using the SLEDGE package on Sturm-Liouville problems having nonempty essential spectra, with Michael Eastham and Charles Fulton, ACM Trans. on Math. Software, 22 (1996), pp. 423-446.
- Accurate Sturm-Liouville eigenfunction computation in mathematical software, in Spectral Theory and Computational Methods, D. Hinton, P. Schafer, eds., Marcel Dekker, New York, 1997, pp. 333-347.
- Error analysis in the approximation of Sturm-Liouville spectral density functions, with C. Fulton, J. Math. Anal. and Appl, 203 (1996), pp. 518-539.
- Fundamentals of Numerical Computing, with L. Shampine and R. Allen, John Wiley & Sons, 1996.
- A stable high order interpolation scheme for superconvergent collocation data, with H. Jin, SIAM J. Sci. Comp., 17 (1996), pp. 714-724.
- An asymptotic numerical method for a class of singular Sturm-Liouville problems, with Y. Xie and C. Fulton, SIAM J. Numer. Anal., 32 (1995), pp. 1658-1676.
- A Sturm separation theorem for a linear 2n-th order self-adjoint differential equation, with Charles Fulton and L. Wu, J. Appl. Math. and Stoch. Analysis, 8 (1995), pp. 29-46.
- Some remarks on the numerical estimation of fractal dimension, Chapter 3 in Fractal Geometry and Its Use in the Earth Sciences, C. Barton and P. La Pointe, eds., Plenum, 1994, pp. 65-75.
- Eigenvalue and eigenfunction asymptotics for regular Sturm-Liouville problems, with C. Fulton, J. Math. Anal. and Appl., 188 (1994), pp. 297-340.
- Parallel computation of Sturm-Liouville spectral density functions, with C. Fulton and W. Shoaff, Parallel Algorithms and Applications, 4 (1994), pp. 41-51.
- Numerical approximation of singular spectral functions arising from the Fourier-Jacobi problem on a half line with continuous spectra, with C. Fulton, in Fourier Analysis: Analytic and Geometric Aspects, , Bray et al, eds., Lecture Notes in Pure and Applied Mathematics, Dekker, 157 (1994), pp. 149-169.
- Achieving global error control in SLEDGE, Colorado School of Mines, Dept. of Math. & CS, report MCS-93-16, 1993.
- Mathematical software for Sturm-Liouville problems, with C. Fulton, ACM Trans. on Math. Software, 19 (1993), pp. 360-376.
- A shape preserving C2 cubic interpolatory spline, IMA J. Numer. Anal., 13 (1993), pp. 493-507.
- Equivalence of various characterizations of the oscillatory/nonoscillatory classification for singular endpoints of 4th order self-adjoint differential equations, with C. Fulton and L. Wu, in Proc. of the World Congress of Nonlinear Analysts '92, ed. by V. Lakshmikantham, de Gruyter, 1996, pp. 1943-1954.
- Performance of the Sturm-Liouville package SLEDGE, with C. Fulton and Y. Xie, Colorado School of Mines, Dept. of Math & CS, report MCS-91-19, 1991.
- Shape preserving interpolation by parametric cubic polynomials, with James C. Ferguson, Computer-Aided Design, 23 (1991), pp. 498-505.
- A User's Guide to the Code SPDNSF, with C. Fulton, in the Proc. of the Focused Research Program on Spectral Theory and Boundary Value Problems, Argonne National Laboratory, Mathematics and Computer Science Division, ANL-87-26, 3 (1989), pp. 77-102.
- Splines and Their Applications, Tech. Report, Dept. of Mathematics, Facultad de Ciencias, Nat. Autonomous Univ. of Mexico, No. 169, 1989.
- Software matemática para problemas de Sturm-Liouville, Vinculos Matematicos, Dept. de Matematicas, Facultad de Ciencias, UNAM, No. 166, 1989.
- On shooting algorithms for calculating Sturm-Liouville eigenvalues, J. of Comp.Phys., 75 (1988), pp. 493-497.
- Stability of local Lagrangian interpolation, J. of Approx. Theory, 73 (1988), pp. 117-127.
- Concise representation of generalized gradients, with M. Osborne and R. Womersley, J. Austral. Math. Soc. Ser. B, 28 (1986), pp. 57-74.
- Interpolation schemes for collocation solutions of two-point boundary value problems, SIAM J. Sci. and Stat. Comp., 7 (1986), pp. 322-333.
- On spline basis selection for solving ordinary differential equations, with U. Ascher and R. Russell, SIAM J. Numer. Anal., 20 (1983), pp. 121-142.
- An analysis of an inverse problem in ordinary differential equations, with R. Allen, SIAM J. Sci. and Stat. Comp., 2 (1981), pp. 176-185.
- Stability analysis of two-dimensional digital recursive filters, with W. Alexander, IEEE Trans. on Circuits and Systems, 27 (1980), pp. 11-15.
- Summary of workshop on basis selection, with R. Sincovec et al, ibid., pp. 263-265.
- An extrapolation method based on solving a sequence of collocation problems, in Codes for Boundary Value Problems in ODE's ,ed. by Bart Childs, Springer, Berlin, 1979, pp. 257-262.
- Alternatives to the exponential spline in tension, Math. Comp., 33 (1979), pp. 1273-1281.
- Numerical methods for eigenvalue problems with eigenparameter in the boundary condition, with Charles Fulton, J. Math. Anal. Appl., 71 (1979), pp. 431-484.
- An algorithm for computing smoothing splines in tension, Computing, 19 (1978), pp. 365-373.
- Properties of splines in tension, J. of Approx. Theory, 17 (1976), pp. 86-96.
- High order approximation of Sturm-Liouville eigenvalues, Numer. Math., 24 (1975), pp. 241-247.
- The approximation of linear functionals and h2-extrapolation, SIAM Review, 17 (1975), pp. 641-651.
- Solving linear boundary value problems by approximating the coefficients, Math. Comp., 27 (1973), pp. 551-561.
- Estimating the eigenvalues of Sturm-Liouville problems by approximating the differential equation, SIAM J. Numer. Anal.,10 (1973), pp. 55-68.

**Funded Research:**

- Development of software for Sturm-Liouville problems, NSF, 04/04/86 - 07/31/90, 25 hours supercomputing time.
- Mathematical software for Sturm-Liouville problems, NSF, 07/01/88 - 12/31/89, $49,595.
- Parallel implementations of SLEDGE (consultant), Florida Institute of Technology, NSF Grant ASC88-21626, 1989-1992.
- Mathematical software for singular Sturm-Liouville problems, NSF, 07/01/89 - 06/30/92, $115,070.
- Stable qualitatively correct interpolants for highly accurate data, NSF, 08/15/94 - 7/31/98, $60,000.
- NIOGEMS - Phase III, BIA, 08/01/97 - 04/30/98, $70,962.
- EPICS Design and CS Programming Laboratory, with Derek Wilson and Robert Knecht, CSM Technology Fee, Fall 1997, $95,000.
- Cheap Sturm-Liouville Spectral Functions, with Charles Fulton and David Pearson, NSF, 08/15/2002 - 07/31/2006, $144,266.
- Estimating Sturm-Liouville Spectral Functions, with David Pearson and Charles Fulton, EPSRC, Visiting Faculty Grant, 05/2004 - 08/2004.

**Selected Presentations**

July 2008: World Congress of Nonlinear Analysts (invited), "Theory and
Numerics for Estimating Spectral Density Functions for Periodic
Potentials on the Half-Line", Orlando.

September 1998: "Superconvergent interpolants for linear two-point
boundary value problems", ACES Supercomputing Conference (invited),
Albuquerque.

March 1998: "Sturm-Liouville software", Univ. Colorado - Boulder.

July 1997: "Computing Sturm-Liouville eigenfunctions", SIAM National
Meeting, Stanford.

March 1996: Barrett Lectures (invited), "Accurate Sturm-Liouville
eigenfunction computation in mathematical software", Knoxville.

August 1994: "Parallelism in the estimation of Sturm-Liouville density
functions", Sandia Nat. Lab.

August 1994: "Parallelism in the estimation of Sturm-Liouville density
functions", Los Alamos Nat. Lab.

January 1994: CPR seminar, "Stable high accuracy interpolants for
boundary value problems", Golden.

July 1993: Gregynog Workshop (invited),"Global error estimation in
SLEDGE", Gregynog, Wales.

April 1993: MAA sectional meeting,"Stable qualitatively correct
interpolants for high accuracy discrete data", Denver.

July 1991: ICIAM international meeting, "Approximation of
Sturm-Liouville eigenvalues and eigenvectors with global error
control", invited Minisymposium talk, Washington DC.

July 1991: ICIAM international meeting, "Asymptotic numerical methods
for Sturm-Liouville equations", invited Minisymposium talk,
Washington DC.

March 1991: Florida Institute of Technology, "A class of hard problems
for Sturm-Liouville solvers"

November 1990: Front Range Computational Circus, "Mathematical
software for Sturm-Liouville problems" , Denver.

July 1990: National SIAM meeting, "Mathematical software for
Sturm-Liouville problems", Chicago.

June 1990: Florida Institute of Technology, "Implementing parallelism
in Sturm-Liouville software"

January 1990: Florida Institute of Technology, "Parallelization in
Sturm-Liouville Software"

August 1989: National Science Foundation, "Mathematical Software for
Sturm-Liouville Problems"

June 1989: Florida Institute of Technology, "Mathematical Software
for Sturm-Liouville Problems"

April 1989: Colorado School of Mines short course on "Applications of
Fractals to Geology"

June 1987: Three talks at the Second Jornada on Mathematical and
Numerical Analysis, University of Guanajuato, "Software for
Sturm-Liouville problems", Guanajuato, Mexico.

June 1987: Argonne National Laboratory, "Algorithms underlying the
code SPDNSF"

April 1987: Michigan Tech. University, "Mathematical software for
Sturm-Liouville problems"

June 1985: Two talks at Argonne National Laboratory, "Estimating the
eigenvalues of Sturm-Liouville problems"

July 1982: Talk at CSIRO, "Monomial bases for solving two-point
boundary value problems", Canberra, Australia.

July 1982: Three lectures at Australian National University,
"Splines and their applications"

February 1982: Regional Conference on Two-Point Boundary Value
Problems, "Variable order collocation methods", invited talk,
Pocatello, Idaho.

September 1979: State ACM Meeting, "A spline method for the
compartmental analysis problem", Elephant Butte, New Mexico.

May 1978: Working Conference on Codes for Two-Point Boundary Value Problems,
"An extrapolation method based on collocation", Houston, Texas.

October 1977: SIAM National Meeting, "Rational alternatives to the
exponential spline in tension",

November 1976: AMS Regional Meeting, "Eigenvalue problems with
eigenparameter in the boundary condition", Albuquerque, New Mexico.

October 1972: SIAM National Meeting, "Solving differential equations
by approximating the coefficients", Austin, Texas.

**Referee/Reviewer for**

ACM Transactions on Mathematical Software, Applied Mathematics Letters,
Applied Numerical Mathematics, Chemical Engineering
Communications, Computer-Aided Geometric Design, Computers and Math.
with Applications, IMA J. Numerical Analysis, J. Approximation Theory,
J. Australian Mathematical Society, J. Computational & Applied Mathematics,
J. Computational Physics, J. Mathematical Analysis & Applications,
Matematica Aplicada e Computacional, Mathematics of Computation,
National Center for Supercomputing Applications, National Scientific
& Educational Research Council (Canada), National Science Foundation,
Numerische Mathematik, Proc. A - Royal Society of Edinburgh,
SIAM J. Numerical Analysis, SIAM J. Scientific Computing

Revision Date: 29 May 2008