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Recent Submissions
CENI New Faculty COE (Spring 2026)
Gary Kirk (CENI, 2025-02-10)
Extending Elman's Bound for GMRES
Embree, Mark P. (Elsevier, 2025-07-24)
If the numerical range of a matrix is contained in the right half of the complex plane, the GMRES algorithm for solving linear systems will reduce the norm of the residual at every iteration. In his Ph.D. dissertation, Howard Elman derived a bound that guarantees convergence. When the numerical range contains the origin, GMRES need not make progress at every step and Elman's bound does not apply, even if all the eigenvalues are located in the right half-plane. However by solving a Lyapunov equation, one can construct an inner product in which the numerical range is contained in the right half-plane. One can then bound GMRES (run in the standard Euclidean norm) by applying Elman's bound in this new inner product, at the cost of a multiplicative constant that characterizes the distortion caused by the change of inner product. Using Lyapunov inverse iteration, one can build a family of such inner products, trading o the location of the numerical range with the size of constant. This approach complements techniques that Greenbaum and colleagues have recently proposed for excising the origin from the numerical range to gain greater insight into the convergence of GMRES for nonnormal matrices.
Polynomial Approximation to the Inverse of a Large Matrix
Embree, Mark P.; Henningsen, Joel A.; Jackson, Jordan; Morgan, Ronald B. (Society for Industrial & Applied Mathematics, 2025-08-25)
The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its approximation to the inverse often seems to track the accuracy of the GMRES iteration. We investigate the quality of this approximation through theory and experiment, noting the practical need to add copies of some polynomial terms to improve stability. To mitigate storage and orthogonalization costs, other approaches have appeal, such as polynomial preconditioned GMRES and deflation of problematic eigenvalues. Applications of such polynomial approximations include solving systems of linear equations with multiple right-hand sides (where the solutions to subsequent problems come simply by multiplying the polynomial against the new right-hand sides) and variance reduction in multilevel Monte Carlo methods.
Longitudinal Relations Between Parents’ Familism Values and Warmth and U.S. Latine Adolescents’ Prosocial Behaviors and the Mediating Role of Adolescents’ Familism Values
Kreidell, Kennedy Jeannette (Virginia Tech, 2025-12-02)
Prosocial behaviors, or actions that are intended to benefit others, are important indicators of social competence and development in adolescence. Latine adolescents living in the United States (U.S. Latines) experience cultural socialization of familism values that may promote the development of prosocial behaviors. Further, parents’ own familism values help promote adolescents’ prosocial behaviors through socializing children toward behaviors that align with the values of support and obligation. Warm parents, in particular, model behaviors that are consistent with familism values and values of prosocial behavior that allow for adolescents to internalize messages of prosocial behavior and be motivated to perform these behaviors themselves. Using large, nationally-representative data from the National Institutes of Health (NIH) Adolescent Brain Cognitive Development (ABCD) Study, this project examined longitudinal relations among parents’ familism values, parental warmth, adolescents’ familism values, and adolescents’ prosocial behaviors. Parents reported on their familism values when adolescents were 10-11 years old and adolescents’ prosocial behavior at 12-13 years. Adolescents reported their parents’ warm and supportive behaviors when they were 10-11 years old, their own familism values at age 11-12 years, and their prosocial behavior at age 12-13 years. Both parents’ own familism values and parental warmth at age 10-11 years were positively related to adolescents’ prosocial behavior at age 12-13 years both directly and indirectly through a positive relation with adolescents’ familism values at age 11-12 years. Findings support cultural socialization theories and prosocial development models as well as have implications for the development of prosocial behaviors among U.S. Latine adolescents.
A System Approach to Optimizing Driver's License Processing: A Descriptive Correlational Study at LTO-7 Lapu-Lapu City, Cebu
Ali, Norhaima U. (Cebu Technological University, 2025-05)
This descriptive correlational study examined the optimization of driver’s license processing at the Land Transportation Office (LTO) in Lapu-Lapu City, Cebu, through a systems approach. The study investigated clients’ perceptions of service efficiency, staff competence, system accessibility, process complexity, client satisfaction, and public trust in LTO services. Data collected from respondents revealed strong agreement on service efficiency, staff competence, and client satisfaction, indicating that clients generally perceive the LTO as providing timely and professional service. However, perceptions of system accessibility showed mixed results, with concerns about difficulties in accessing online appointment systems. Notably, public trust in LTO and government services was consistently low, highlighting a critical gap between service delivery satisfaction and institutional trust. Multiple regression analysis further revealed that demographic variables (age, gender, educational attainment, length of membership) and service-related factors did not significantly predict client satisfaction or public trust. Based on these findings, the study proposes an Enhanced Service and Trust Optimization Program (ESTOP) comprising five strategic initiatives: Client Accessibility Enhancement, Simplified Licensing Orientation, Integrity and Transparency Summit, Gender Sensitivity Training, and Public Service Ethics & Anti-Corruption Workshops. This program aims to bridge the disconnect between service satisfaction and public trust by addressing accessibility challenges, promoting transparency, and fostering ethical conduct among staff. The study underscores the importance of a holistic system approach to public service optimization, combining operational efficiency with transparency and community engagement to rebuild trust. Implications for policy and practice suggest that enhancing public trust requires continuous efforts beyond service delivery improvements emphasizing institutional integrity and client-centered governance.