Based on the simplified FaST-LMM, wherein genomic variance is replaced with heritability, we have significantly improved computational efficiency by implementing rapid R/fastLmPure to statistically infer the genetic effects of tested SNPs and focus on large or highly significant SNPs obtained using the EMMAX algorithm. For a genome-wide mixed-model association analysis, we introduce a barebones linear model fitting function called fastLmPure from the R/RcppArmadillo package for the rapid estimation of single nucleotide polymorphism (SNP) effects and the maximum likelihood values of factored spectrally transformed linear mixed models (FaST-LMM). Starting from the estimated genomic heritability of quantitative traits under a null model without quantitative trait nucleotides, maximum likelihood estimations of the polygenic heritabilities of candidate markers consume the same time as approximately four rounds of genome-wide regression scans. When focusing only on SNPs with large effects or high significance levels, as estimated by the efficient mixed-model association expedited algorithm, the run time of genome-wide mixed-model association analysis is reduced to at most two rounds of genome-wide regression scans. We have developed a novel software application called Single-RunKing to transform nonlinear mixed-model association analyses into barebones linear regression scans. Based on a realised relationship matrix calculated using genome-wide markers, Single-RunKing saves significantly computation time, as compared with the FaST-LMM that optimises the variance ratios of polygenic variances to residual variances using the R/lm function.